Movie recommendation system.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "import surprise\n",
    "\n",
    "from surprise import SVD, SVDpp, SlopeOne, NMF, NormalPredictor, KNNBasic, KNNBaseline, KNNWithMeans, KNNWithZScore, BaselineOnly, CoClustering\n",
    "from surprise.model_selection import train_test_split, cross_validate, GridSearchCV  #not as same as the cross_validation from scikit learn?\n",
    "from surprise import Reader, Dataset, accuracy\n",
    "from surprise import dump\n",
    "\n",
    "from sklearn.metrics.pairwise import cosine_similarity\n",
    "\n",
    "from sklearn import preprocessing\n",
    "\n",
    "#libraries for data visualization\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.pylab as pylab\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "#sns.set_palette('Set2')\n",
    "sns.set_color_codes(\"pastel\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load built in data from surprise library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = surprise.Dataset.load_builtin('ml-100k')   #Dataset.load_builtin('ml-100k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user</th>\n",
       "      <th>item</th>\n",
       "      <th>rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>196</td>\n",
       "      <td>242</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>186</td>\n",
       "      <td>302</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>377</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>244</td>\n",
       "      <td>51</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>166</td>\n",
       "      <td>346</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>298</td>\n",
       "      <td>474</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>115</td>\n",
       "      <td>265</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>253</td>\n",
       "      <td>465</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>305</td>\n",
       "      <td>451</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>6</td>\n",
       "      <td>86</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  user item  rate\n",
       "0  196  242   3.0\n",
       "1  186  302   3.0\n",
       "2   22  377   1.0\n",
       "3  244   51   2.0\n",
       "4  166  346   1.0\n",
       "5  298  474   4.0\n",
       "6  115  265   2.0\n",
       "7  253  465   5.0\n",
       "8  305  451   3.0\n",
       "9    6   86   3.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(data.raw_ratings, columns=[\"user\", \"item\", \"rate\", \"id\"])\n",
    "del df[\"id\"]\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of users:  943\n",
      "number of movies:  1682\n"
     ]
    }
   ],
   "source": [
    "print(\"number of users: \", df.user.nunique())\n",
    "print(\"number of movies: \", df.item.nunique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3., 4., 5.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort( df.rate.unique() )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "user    0\n",
       "item    0\n",
       "rate    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>item</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>452</td>\n",
       "      <td>3.878319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>89</td>\n",
       "      <td>3.831461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>508</td>\n",
       "      <td>4.155512</td>\n",
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       "      <th>1000</th>\n",
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       "      <td>3.000000</td>\n",
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       "    <tr>\n",
       "      <th>1001</th>\n",
       "      <td>17</td>\n",
       "      <td>2.000000</td>\n",
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       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>31</td>\n",
       "      <td>3.161290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>14</td>\n",
       "      <td>2.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>16</td>\n",
       "      <td>2.125000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>16</td>\n",
       "      <td>2.562500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>10</td>\n",
       "      <td>2.800000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1682 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      rate          \n",
       "     count      mean\n",
       "item                \n",
       "1      452  3.878319\n",
       "10      89  3.831461\n",
       "100    508  4.155512\n",
       "1000    10  3.000000\n",
       "1001    17  2.000000\n",
       "...    ...       ...\n",
       "995     31  3.161290\n",
       "996     14  2.500000\n",
       "997     16  2.125000\n",
       "998     16  2.562500\n",
       "999     10  2.800000\n",
       "\n",
       "[1682 rows x 2 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('item')[['rate']].agg(['count', 'mean'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "      <td>5.0</td>\n",
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       "      <th>1293</th>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
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       "      <th>1189</th>\n",
       "      <td>3</td>\n",
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       "      <th>1653</th>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
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       "    <tr>\n",
       "      <th>1467</th>\n",
       "      <td>2</td>\n",
       "      <td>5.0</td>\n",
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      ],
      "text/plain": [
       "      rate     \n",
       "     count mean\n",
       "item           \n",
       "1500     2  5.0\n",
       "1293     3  5.0\n",
       "1189     3  5.0\n",
       "1653     1  5.0\n",
       "1467     2  5.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('item')[['rate']].agg(['count', 'mean']).sort_values( by=('rate',  'mean'), ascending=False)[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mean_rating = df.groupby('item')[['rate']].mean()\n",
    "lowest_rated = mean_rating['rate'].idxmin()\n",
    "df.loc[df['item'] == lowest_rated]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">rate</th>\n",
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       "    <tr>\n",
       "      <th>item</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1408</th>\n",
       "      <td>3</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1671</th>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1557</th>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>599</th>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>1678</th>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      rate     \n",
       "     count mean\n",
       "item           \n",
       "1408     3  1.0\n",
       "1671     1  1.0\n",
       "1557     1  1.0\n",
       "599      1  1.0\n",
       "1678     1  1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('item')[['rate']].agg(['count', 'mean']).sort_values(by=('rate', 'mean'), ascending=True)[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "highest_rated = mean_rating['rate'].idxmax()\n",
    "df.loc[df['item'] == highest_rated]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### weighted average ratings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "      <th>1</th>\n",
       "      <td>452</td>\n",
       "      <td>3.878319</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>89</td>\n",
       "      <td>3.831461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>508</td>\n",
       "      <td>4.155512</td>\n",
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       "      <th>1000</th>\n",
       "      <td>10</td>\n",
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       "      <th>1001</th>\n",
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      "text/plain": [
       "      count      mean\n",
       "item                 \n",
       "1       452  3.878319\n",
       "10       89  3.831461\n",
       "100     508  4.155512\n",
       "1000     10  3.000000\n",
       "1001     17  2.000000"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movie_stats = df.groupby('item')[['rate']].agg(['count', 'mean'])\n",
    "movie_stats.columns = movie_stats.columns.droplevel()\n",
    "movie_stats.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = movie_stats['count'].mean()\n",
    "m = movie_stats['mean'].mean()\n",
    "\n",
    "def bayesian_avg(ratings):\n",
    "    bayesian_avg = (C*m+ratings.sum())/(C+ratings.count())\n",
    "    return bayesian_avg\n",
    "\n",
    "bayesian_avg_ratings = df.groupby('item')['rate'].agg(bayesian_avg).reset_index()\n",
    "bayesian_avg_ratings.columns = ['item', 'bayesian_avg']\n",
    "movie_stats = movie_stats.merge(bayesian_avg_ratings, on='item')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "      <th>1128</th>\n",
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       "      <td>298</td>\n",
       "      <td>4.466443</td>\n",
       "      <td>4.235186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1283</th>\n",
       "      <td>64</td>\n",
       "      <td>283</td>\n",
       "      <td>4.445230</td>\n",
       "      <td>4.207526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1109</th>\n",
       "      <td>483</td>\n",
       "      <td>243</td>\n",
       "      <td>4.456790</td>\n",
       "      <td>4.185378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>223</th>\n",
       "      <td>12</td>\n",
       "      <td>267</td>\n",
       "      <td>4.385768</td>\n",
       "      <td>4.147243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>301</th>\n",
       "      <td>127</td>\n",
       "      <td>413</td>\n",
       "      <td>4.283293</td>\n",
       "      <td>4.131374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1660</th>\n",
       "      <td>98</td>\n",
       "      <td>390</td>\n",
       "      <td>4.289744</td>\n",
       "      <td>4.129197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>766</th>\n",
       "      <td>174</td>\n",
       "      <td>420</td>\n",
       "      <td>4.252381</td>\n",
       "      <td>4.106513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1243</th>\n",
       "      <td>603</td>\n",
       "      <td>209</td>\n",
       "      <td>4.387560</td>\n",
       "      <td>4.097105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>921</th>\n",
       "      <td>313</td>\n",
       "      <td>350</td>\n",
       "      <td>4.245714</td>\n",
       "      <td>4.075877</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     item  count      mean  bayesian_avg\n",
       "1128   50    583  4.358491      4.239812\n",
       "926   318    298  4.466443      4.235186\n",
       "1283   64    283  4.445230      4.207526\n",
       "1109  483    243  4.456790      4.185378\n",
       "223    12    267  4.385768      4.147243\n",
       "301   127    413  4.283293      4.131374\n",
       "1660   98    390  4.289744      4.129197\n",
       "766   174    420  4.252381      4.106513\n",
       "1243  603    209  4.387560      4.097105\n",
       "921   313    350  4.245714      4.075877"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movie_stats.sort_values(by='bayesian_avg', ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Collaborative filtering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## user-item matrix  (user utility matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>100</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>3.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>5.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>5.0</td>\n",
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       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>4.0</td>\n",
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       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>943 rows × 1682 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "item    1   10  100  1000  1001  1002  1003  1004  1005  1006  ...  990  991  \\\n",
       "user                                                           ...             \n",
       "1     5.0  3.0  5.0   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "10    4.0  NaN  5.0   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "100   NaN  NaN  NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  3.0  NaN   \n",
       "101   3.0  NaN  NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "102   3.0  NaN  NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "...   ...  ...  ...   ...   ...   ...   ...   ...   ...   ...  ...  ...  ...   \n",
       "95    5.0  NaN  NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "96    5.0  NaN  5.0   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "97    4.0  NaN  2.0   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "98    NaN  NaN  NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "99    4.0  NaN  5.0   NaN   NaN   NaN   NaN   NaN   NaN   NaN  ...  NaN  NaN   \n",
       "\n",
       "item  992  993  994  995  996  997  998  999  \n",
       "user                                          \n",
       "1     NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "10    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "100   NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "101   NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "102   NaN  2.0  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "...   ...  ...  ...  ...  ...  ...  ...  ...  \n",
       "95    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "96    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "97    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "98    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "99    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  \n",
       "\n",
       "[943 rows x 1682 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_table = df.pivot_table(index='user', columns='item',values='rate')\n",
    "df_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>943 rows × 1682 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "item    1   10  100  1000  1001  1002  1003  1004  1005  1006  ...  990  991  \\\n",
       "user                                                           ...             \n",
       "1     5.0  3.0  5.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "10    4.0  0.0  5.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "100   0.0  0.0  0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  3.0  0.0   \n",
       "101   3.0  0.0  0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "102   3.0  0.0  0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "...   ...  ...  ...   ...   ...   ...   ...   ...   ...   ...  ...  ...  ...   \n",
       "95    5.0  0.0  0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "96    5.0  0.0  5.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "97    4.0  0.0  2.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "98    0.0  0.0  0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "99    4.0  0.0  5.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0  ...  0.0  0.0   \n",
       "\n",
       "item  992  993  994  995  996  997  998  999  \n",
       "user                                          \n",
       "1     0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "10    0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "100   0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "101   0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "102   0.0  2.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "...   ...  ...  ...  ...  ...  ...  ...  ...  \n",
       "95    0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "96    0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "97    0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "98    0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "99    0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  \n",
       "\n",
       "[943 rows x 1682 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_pvt = df_table.fillna(0)\n",
    "df_pvt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sparsity calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sparsity:  6.30%\n"
     ]
    }
   ],
   "source": [
    "df_table.values\n",
    "\n",
    "np.isnan( df_table.values  ).sum()\n",
    "\n",
    "np.prod(df_table.values.shape)\n",
    "\n",
    "np.prod(df_table.shape)\n",
    "\n",
    "#sparsity of matrix = Number of Empty cells / Total Number of cells.\n",
    "sparsity = 1 - np.isnan(df_table.values).sum() / np.prod(df_table.shape)\n",
    "print(\"Sparsity: \", '{:2.2%}'.format(sparsity) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Only 6.3% of cells in the user-item matrix are populated with ratings. A general rule of thumb is that your matrix sparsity should be no lower than 0.5% to generate decent results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## similarity based on cosine metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.630601</td>\n",
       "      <td>0.114364</td>\n",
       "      <td>0.109701</td>\n",
       "      <td>0.084998</td>\n",
       "      <td>0.100452</td>\n",
       "      <td>0.061399</td>\n",
       "      <td>0.093729</td>\n",
       "      <td>0.101029</td>\n",
       "      <td>...</td>\n",
       "      <td>0.085165</td>\n",
       "      <td>0.091251</td>\n",
       "      <td>0.070873</td>\n",
       "      <td>0.353507</td>\n",
       "      <td>0.060461</td>\n",
       "      <td>0.085890</td>\n",
       "      <td>0.098793</td>\n",
       "      <td>0.141426</td>\n",
       "      <td>0.138101</td>\n",
       "      <td>0.099471</td>\n",
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       "      <th>10</th>\n",
       "      <td>0.273935</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.336233</td>\n",
       "      <td>0.044153</td>\n",
       "      <td>0.053510</td>\n",
       "      <td>0.025705</td>\n",
       "      <td>0.046341</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.224322</td>\n",
       "      <td>0.130158</td>\n",
       "      <td>...</td>\n",
       "      <td>0.085546</td>\n",
       "      <td>0.081927</td>\n",
       "      <td>0.067685</td>\n",
       "      <td>0.027119</td>\n",
       "      <td>0.048401</td>\n",
       "      <td>0.123714</td>\n",
       "      <td>0.007909</td>\n",
       "      <td>0.033473</td>\n",
       "      <td>0.121554</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.630601</td>\n",
       "      <td>0.336233</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.084698</td>\n",
       "      <td>0.144486</td>\n",
       "      <td>0.084889</td>\n",
       "      <td>0.061514</td>\n",
       "      <td>0.097603</td>\n",
       "      <td>0.153229</td>\n",
       "      <td>0.168087</td>\n",
       "      <td>...</td>\n",
       "      <td>0.089523</td>\n",
       "      <td>0.098840</td>\n",
       "      <td>0.075603</td>\n",
       "      <td>0.191055</td>\n",
       "      <td>0.090889</td>\n",
       "      <td>0.119886</td>\n",
       "      <td>0.053259</td>\n",
       "      <td>0.139800</td>\n",
       "      <td>0.127146</td>\n",
       "      <td>0.038349</td>\n",
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       "      <th>1000</th>\n",
       "      <td>0.114364</td>\n",
       "      <td>0.044153</td>\n",
       "      <td>0.084698</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.381626</td>\n",
       "      <td>0.198191</td>\n",
       "      <td>0.044662</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.042403</td>\n",
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       "      <td>0.021277</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.456630</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.365864</td>\n",
       "      <td>0.129040</td>\n",
       "      <td>0.288370</td>\n",
       "      <td>0.521862</td>\n",
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       "      <th>1001</th>\n",
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       "      <td>0.381626</td>\n",
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       "      <td>0.000000</td>\n",
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       "      <td>0.025786</td>\n",
       "      <td>0.016116</td>\n",
       "      <td>0.379473</td>\n",
       "      <td>0.081088</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.005315</td>\n",
       "      <td>0.128093</td>\n",
       "      <td>0.260643</td>\n",
       "      <td>0.183478</td>\n",
       "      <td>0.210819</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>0.085890</td>\n",
       "      <td>0.123714</td>\n",
       "      <td>0.119886</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.005315</td>\n",
       "      <td>0.008511</td>\n",
       "      <td>0.046029</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.058251</td>\n",
       "      <td>0.032776</td>\n",
       "      <td>...</td>\n",
       "      <td>0.106898</td>\n",
       "      <td>0.154184</td>\n",
       "      <td>0.033615</td>\n",
       "      <td>0.014366</td>\n",
       "      <td>0.128201</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.016624</td>\n",
       "      <td>0.027862</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>0.098793</td>\n",
       "      <td>0.007909</td>\n",
       "      <td>0.053259</td>\n",
       "      <td>0.365864</td>\n",
       "      <td>0.128093</td>\n",
       "      <td>0.015778</td>\n",
       "      <td>0.142220</td>\n",
       "      <td>0.010056</td>\n",
       "      <td>0.005400</td>\n",
       "      <td>0.006751</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.123177</td>\n",
       "      <td>0.014854</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.154092</td>\n",
       "      <td>0.137742</td>\n",
       "      <td>0.301202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>0.141426</td>\n",
       "      <td>0.033473</td>\n",
       "      <td>0.139800</td>\n",
       "      <td>0.129040</td>\n",
       "      <td>0.260643</td>\n",
       "      <td>0.016695</td>\n",
       "      <td>0.150482</td>\n",
       "      <td>0.138329</td>\n",
       "      <td>0.005713</td>\n",
       "      <td>0.007144</td>\n",
       "      <td>...</td>\n",
       "      <td>0.032260</td>\n",
       "      <td>0.050408</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.098631</td>\n",
       "      <td>0.015717</td>\n",
       "      <td>0.016624</td>\n",
       "      <td>0.154092</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.081981</td>\n",
       "      <td>0.186824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>0.138101</td>\n",
       "      <td>0.121554</td>\n",
       "      <td>0.127146</td>\n",
       "      <td>0.288370</td>\n",
       "      <td>0.183478</td>\n",
       "      <td>0.083943</td>\n",
       "      <td>0.176552</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.143636</td>\n",
       "      <td>0.137690</td>\n",
       "      <td>...</td>\n",
       "      <td>0.022529</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.276289</td>\n",
       "      <td>0.103319</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.027862</td>\n",
       "      <td>0.137742</td>\n",
       "      <td>0.081981</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.055258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>0.099471</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.038349</td>\n",
       "      <td>0.521862</td>\n",
       "      <td>0.210819</td>\n",
       "      <td>0.067516</td>\n",
       "      <td>0.060858</td>\n",
       "      <td>0.010758</td>\n",
       "      <td>0.005776</td>\n",
       "      <td>0.007223</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.033976</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.032053</td>\n",
       "      <td>0.015891</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.301202</td>\n",
       "      <td>0.186824</td>\n",
       "      <td>0.055258</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1682 rows × 1682 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "item         1        10       100      1000      1001      1002      1003  \\\n",
       "item                                                                         \n",
       "1     1.000000  0.273935  0.630601  0.114364  0.109701  0.084998  0.100452   \n",
       "10    0.273935  1.000000  0.336233  0.044153  0.053510  0.025705  0.046341   \n",
       "100   0.630601  0.336233  1.000000  0.084698  0.144486  0.084889  0.061514   \n",
       "1000  0.114364  0.044153  0.084698  1.000000  0.381626  0.198191  0.044662   \n",
       "1001  0.109701  0.053510  0.144486  0.381626  1.000000  0.192154  0.014434   \n",
       "...        ...       ...       ...       ...       ...       ...       ...   \n",
       "995   0.085890  0.123714  0.119886  0.000000  0.005315  0.008511  0.046029   \n",
       "996   0.098793  0.007909  0.053259  0.365864  0.128093  0.015778  0.142220   \n",
       "997   0.141426  0.033473  0.139800  0.129040  0.260643  0.016695  0.150482   \n",
       "998   0.138101  0.121554  0.127146  0.288370  0.183478  0.083943  0.176552   \n",
       "999   0.099471  0.000000  0.038349  0.521862  0.210819  0.067516  0.060858   \n",
       "\n",
       "item      1004      1005      1006  ...       990       991       992  \\\n",
       "item                                ...                                 \n",
       "1     0.061399  0.093729  0.101029  ...  0.085165  0.091251  0.070873   \n",
       "10    0.000000  0.224322  0.130158  ...  0.085546  0.081927  0.067685   \n",
       "100   0.097603  0.153229  0.168087  ...  0.089523  0.098840  0.075603   \n",
       "1000  0.000000  0.000000  0.042403  ...  0.021277  0.000000  0.456630   \n",
       "1001  0.000000  0.000000  0.000000  ...  0.025786  0.016116  0.379473   \n",
       "...        ...       ...       ...  ...       ...       ...       ...   \n",
       "995   0.000000  0.058251  0.032776  ...  0.106898  0.154184  0.033615   \n",
       "996   0.010056  0.005400  0.006751  ...  0.000000  0.000000  0.000000   \n",
       "997   0.138329  0.005713  0.007144  ...  0.032260  0.050408  0.000000   \n",
       "998   0.000000  0.143636  0.137690  ...  0.022529  0.000000  0.276289   \n",
       "999   0.010758  0.005776  0.007223  ...  0.000000  0.033976  0.000000   \n",
       "\n",
       "item       993       994       995       996       997       998       999  \n",
       "item                                                                        \n",
       "1     0.353507  0.060461  0.085890  0.098793  0.141426  0.138101  0.099471  \n",
       "10    0.027119  0.048401  0.123714  0.007909  0.033473  0.121554  0.000000  \n",
       "100   0.191055  0.090889  0.119886  0.053259  0.139800  0.127146  0.038349  \n",
       "1000  0.104545  0.000000  0.000000  0.365864  0.129040  0.288370  0.521862  \n",
       "1001  0.081088  0.000000  0.005315  0.128093  0.260643  0.183478  0.210819  \n",
       "...        ...       ...       ...       ...       ...       ...       ...  \n",
       "995   0.014366  0.128201  1.000000  0.000000  0.016624  0.027862  0.000000  \n",
       "996   0.123177  0.014854  0.000000  1.000000  0.154092  0.137742  0.301202  \n",
       "997   0.098631  0.015717  0.016624  0.154092  1.000000  0.081981  0.186824  \n",
       "998   0.103319  0.000000  0.027862  0.137742  0.081981  1.000000  0.055258  \n",
       "999   0.032053  0.015891  0.000000  0.301202  0.186824  0.055258  1.000000  \n",
       "\n",
       "[1682 rows x 1682 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_item = df.pivot_table(index='item', columns='user',values='rate').fillna(0)\n",
    "\n",
    "item_similarity = pd.DataFrame(cosine_similarity(df_item), index=df_item.index, columns=df_item.index)\n",
    "item_similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <td>0.135963</td>\n",
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       "      <th>10</th>\n",
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       "      <td>0.090305</td>\n",
       "      <td>0.212330</td>\n",
       "      <td>0.221860</td>\n",
       "      <td>0.375380</td>\n",
       "      <td>0.341416</td>\n",
       "      <td>0.301478</td>\n",
       "      <td>0.140115</td>\n",
       "      <td>0.193943</td>\n",
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       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.057354</td>\n",
       "      <td>0.066987</td>\n",
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       "      <td>0.012998</td>\n",
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       "      <td>0.000000</td>\n",
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       "      <th>102</th>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.468911</td>\n",
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       "      <td>0.036854</td>\n",
       "      <td>0.180604</td>\n",
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       "      <td>0.230296</td>\n",
       "      <td>0.144948</td>\n",
       "      <td>0.019579</td>\n",
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       "      <td>0.010945</td>\n",
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       "      <td>0.133712</td>\n",
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       "      <th>96</th>\n",
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       "      <td>0.000000</td>\n",
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       "      <td>0.342054</td>\n",
       "      <td>0.276660</td>\n",
       "      <td>0.110265</td>\n",
       "      <td>0.231118</td>\n",
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       "      <td>0.345199</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.308487</td>\n",
       "      <td>0.074055</td>\n",
       "      <td>0.216023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.352280</td>\n",
       "      <td>0.301478</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.073269</td>\n",
       "      <td>0.301406</td>\n",
       "      <td>0.148177</td>\n",
       "      <td>0.060202</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.155511</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.305776</td>\n",
       "      <td>0.291914</td>\n",
       "      <td>0.150569</td>\n",
       "      <td>0.220158</td>\n",
       "      <td>0.257559</td>\n",
       "      <td>0.343122</td>\n",
       "      <td>0.308487</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.119453</td>\n",
       "      <td>0.160602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.135963</td>\n",
       "      <td>0.140115</td>\n",
       "      <td>0.006082</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.169144</td>\n",
       "      <td>0.030079</td>\n",
       "      <td>0.024732</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.181077</td>\n",
       "      <td>0.029806</td>\n",
       "      <td>...</td>\n",
       "      <td>0.141533</td>\n",
       "      <td>0.152999</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.124439</td>\n",
       "      <td>0.066392</td>\n",
       "      <td>0.133712</td>\n",
       "      <td>0.074055</td>\n",
       "      <td>0.119453</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.079174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.281790</td>\n",
       "      <td>0.193943</td>\n",
       "      <td>0.192041</td>\n",
       "      <td>0.360147</td>\n",
       "      <td>0.294568</td>\n",
       "      <td>0.246592</td>\n",
       "      <td>0.403630</td>\n",
       "      <td>0.127408</td>\n",
       "      <td>0.169480</td>\n",
       "      <td>0.104562</td>\n",
       "      <td>...</td>\n",
       "      <td>0.333846</td>\n",
       "      <td>0.313490</td>\n",
       "      <td>0.263907</td>\n",
       "      <td>0.169623</td>\n",
       "      <td>0.360144</td>\n",
       "      <td>0.278597</td>\n",
       "      <td>0.216023</td>\n",
       "      <td>0.160602</td>\n",
       "      <td>0.079174</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>943 rows × 943 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "user         1        10       100       101       102       103       104  \\\n",
       "user                                                                         \n",
       "1     1.000000  0.376544  0.057354  0.154457  0.397145  0.226111  0.231134   \n",
       "10    0.376544  1.000000  0.066987  0.030877  0.288020  0.145788  0.156615   \n",
       "100   0.057354  0.066987  1.000000  0.012998  0.171988  0.055922  0.375736   \n",
       "101   0.154457  0.030877  0.012998  1.000000  0.153750  0.321378  0.268215   \n",
       "102   0.397145  0.288020  0.171988  0.153750  1.000000  0.237494  0.215930   \n",
       "...        ...       ...       ...       ...       ...       ...       ...   \n",
       "95    0.468911  0.375380  0.036854  0.180604  0.416339  0.230296  0.144948   \n",
       "96    0.361273  0.341416  0.000000  0.086543  0.281648  0.226449  0.099971   \n",
       "97    0.352280  0.301478  0.000000  0.073269  0.301406  0.148177  0.060202   \n",
       "98    0.135963  0.140115  0.006082  0.000000  0.169144  0.030079  0.024732   \n",
       "99    0.281790  0.193943  0.192041  0.360147  0.294568  0.246592  0.403630   \n",
       "\n",
       "user       105       106       107  ...        94       940       941  \\\n",
       "user                                ...                                 \n",
       "1     0.102414  0.288715  0.080152  ...  0.480574  0.314072  0.148617   \n",
       "10    0.077478  0.284969  0.095741  ...  0.418951  0.342961  0.090305   \n",
       "100   0.507451  0.041973  0.329853  ...  0.090008  0.289131  0.099363   \n",
       "101   0.037979  0.035617  0.031846  ...  0.160808  0.083545  0.237333   \n",
       "102   0.185148  0.123308  0.128144  ...  0.439064  0.323743  0.164963   \n",
       "...        ...       ...       ...  ...       ...       ...       ...   \n",
       "95    0.019579  0.278008  0.010945  ...  0.529910  0.330689  0.110761   \n",
       "96    0.000000  0.158699  0.000000  ...  0.342054  0.276660  0.110265   \n",
       "97    0.000000  0.155511  0.000000  ...  0.305776  0.291914  0.150569   \n",
       "98    0.000000  0.181077  0.029806  ...  0.141533  0.152999  0.000000   \n",
       "99    0.127408  0.169480  0.104562  ...  0.333846  0.313490  0.263907   \n",
       "\n",
       "user       942       943        95        96        97        98        99  \n",
       "user                                                                        \n",
       "1     0.179508  0.398175  0.468911  0.361273  0.352280  0.135963  0.281790  \n",
       "10    0.212330  0.221860  0.375380  0.341416  0.301478  0.140115  0.193943  \n",
       "100   0.237968  0.000000  0.036854  0.000000  0.000000  0.006082  0.192041  \n",
       "101   0.081874  0.232549  0.180604  0.086543  0.073269  0.000000  0.360147  \n",
       "102   0.201437  0.383536  0.416339  0.281648  0.301406  0.169144  0.294568  \n",
       "...        ...       ...       ...       ...       ...       ...       ...  \n",
       "95    0.247625  0.400270  1.000000  0.345199  0.343122  0.133712  0.278597  \n",
       "96    0.231118  0.288281  0.345199  1.000000  0.308487  0.074055  0.216023  \n",
       "97    0.220158  0.257559  0.343122  0.308487  1.000000  0.119453  0.160602  \n",
       "98    0.124439  0.066392  0.133712  0.074055  0.119453  1.000000  0.079174  \n",
       "99    0.169623  0.360144  0.278597  0.216023  0.160602  0.079174  1.000000  \n",
       "\n",
       "[943 rows x 943 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_table = df.pivot_table(index='user', columns='item',values='rate')# <- not to use\n",
    "df_pvt = df_table.fillna(0)\n",
    "#df_pvt = df_pvt.fillna(df_pvt.mean(axis=0))\n",
    "\n",
    "user_similarity = pd.DataFrame(cosine_similarity(df_pvt), index=df_pvt.index, columns=df_pvt.index)\n",
    "user_similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_similar_user(user_id):\n",
    "    return user_similarity[user_id].sort_values(ascending=False)[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "user\n",
       "100    1.000000\n",
       "863    0.621852\n",
       "784    0.600292\n",
       "616    0.589742\n",
       "856    0.580211\n",
       "Name: 100, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_similar_user(\"100\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_similar_item(item_id):\n",
    "    return item_similarity[item_id].sort_values(ascending=False)[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "item\n",
       "10     1.000000\n",
       "190    0.400624\n",
       "20     0.397113\n",
       "582    0.385038\n",
       "52     0.377012\n",
       "Name: 10, dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_similar_item('10')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pick a model\n",
    "\n",
    "Matric factorization. factorize the user-itm matrix to get 2 latent factor matrics:\n",
    "    - user-factor matrix\n",
    "    - item -factor matric\n",
    "\n",
    "Algorithms for matric factorization:\n",
    "    - Alternating Least Squares (ALS)\n",
    "    - Stochastic Gradient Descent (SGD)\n",
    "    - Singular Value Decompostion (SVD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "cross_validate(SVD(), np.array(df_table_norm), \n",
    "               measures=['rmse'], cv=3, verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'test_rmse': array([0.94296502, 0.94330743, 0.94886051]),\n",
       " 'fit_time': (2.8758509159088135, 2.724466323852539, 2.7523820400238037),\n",
       " 'test_time': (0.1947157382965088, 0.189835786819458, 0.22121715545654297)}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_validate(SVD(), data, measures=['rmse'], cv=3, verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating biases using als...\n",
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Estimating biases using als...\n",
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Estimating biases using als...\n",
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Computing the msd similarity matrix...\n",
      "Done computing similarity matrix.\n",
      "Estimating biases using als...\n",
      "Estimating biases using als...\n",
      "Estimating biases using als...\n"
     ]
    }
   ],
   "source": [
    "benchmark = []\n",
    "\n",
    "for algo in [SVD(), KNNBaseline(), KNNBasic(), BaselineOnly()]:\n",
    "    results = cross_validate(algo, data, measures=['rmse'], \n",
    "                             cv=3, verbose=False)\n",
    "    \n",
    "    tmp = pd.DataFrame.from_dict(results).mean(axis=0)\n",
    "    tmp = tmp.append(pd.Series([str(algo).split('.')[-1]] , index=['Algorithm']))\n",
    "    benchmark.append(tmp)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>test_rmse</th>\n",
       "      <th>fit_time</th>\n",
       "      <th>test_time</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Algorithm</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>KNNBaseline object at 0x7fa14e02f438&gt;</th>\n",
       "      <td>0.935338</td>\n",
       "      <td>0.298640</td>\n",
       "      <td>4.868870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SVD object at 0x7fa14e02f390&gt;</th>\n",
       "      <td>0.945553</td>\n",
       "      <td>2.990437</td>\n",
       "      <td>0.196380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BaselineOnly object at 0x7fa14e02f4a8&gt;</th>\n",
       "      <td>0.946474</td>\n",
       "      <td>0.096433</td>\n",
       "      <td>0.183285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KNNBasic object at 0x7fa14e02f470&gt;</th>\n",
       "      <td>0.988102</td>\n",
       "      <td>0.199348</td>\n",
       "      <td>4.140078</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                        test_rmse  fit_time  test_time\n",
       "Algorithm                                                             \n",
       "KNNBaseline object at 0x7fa14e02f438>    0.935338  0.298640   4.868870\n",
       "SVD object at 0x7fa14e02f390>            0.945553  2.990437   0.196380\n",
       "BaselineOnly object at 0x7fa14e02f4a8>   0.946474  0.096433   0.183285\n",
       "KNNBasic object at 0x7fa14e02f470>       0.988102  0.199348   4.140078"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(benchmark).set_index('Algorithm').sort_values('test_rmse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pick an evaluation metric\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hyperparameter Tuning\n",
    "    - try to tune k (# of factors)\n",
    "    - try to tune lambda regularization parameter\n",
    "  \n",
    "methods: \n",
    "- Grid Search \n",
    "    sklearn.model_selection.GridSearchCV\n",
    "- Random Search\n",
    "    sklearn.model_selection.RandomizedSearchCV\n",
    "- Sequential Model-Based Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model training\n",
    "train model with optimal hyperparameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Post-processing\n",
    "sort predicted ratings and get top N\n",
    "Filter out items that a user has already has seen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation\n",
    "- A/B testing from users - most optimal method\n",
    "- Traditional ML. \n",
    "- Recommendation systems. \n",
    "\n",
    "Precision and Recall"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# model application"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "train, test = train_test_split(df, test_size=0.25, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "trainset = data.build_full_trainset()\n",
    "testset = trainset.build_testset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "algo = SVD()\n",
    "algo.fit(trainset)\n",
    "\n",
    "predictions = algo.test(testset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 0.6745\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.67448754412497"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy.rmse(predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Prediction(uid='196', iid='242', r_ui=3.0, est=3.6567667811191837, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='393', r_ui=4.0, est=3.6276016570863536, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='381', r_ui=4.0, est=3.443696674250781, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='251', r_ui=3.0, est=4.007054282777309, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='655', r_ui=5.0, est=4.315959595824702, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='67', r_ui=5.0, est=3.4016308937817024, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='306', r_ui=4.0, est=3.8572543249215183, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='238', r_ui=4.0, est=3.5731047747907976, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='663', r_ui=5.0, est=4.270789097980604, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='111', r_ui=4.0, est=3.8260962671645804, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='580', r_ui=2.0, est=3.0140993745772855, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='25', r_ui=4.0, est=3.491256453180316, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='286', r_ui=5.0, est=3.7485839583267064, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='94', r_ui=3.0, est=3.1124428443139798, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='692', r_ui=5.0, est=4.055436881697284, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='8', r_ui=5.0, est=4.289621953248107, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='428', r_ui=4.0, est=3.9673173826636443, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='1118', r_ui=4.0, est=3.597588773777325, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='70', r_ui=3.0, est=3.3413913945701865, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='66', r_ui=3.0, est=3.4878597840741814, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='257', r_ui=2.0, est=3.288862760002338, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='108', r_ui=4.0, est=3.353767152012686, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='202', r_ui=3.0, est=3.7213346854189004, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='340', r_ui=3.0, est=3.212988092767459, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='287', r_ui=3.0, est=3.420482526930412, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='116', r_ui=3.0, est=3.666064347672098, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='382', r_ui=4.0, est=3.7299044954096825, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='285', r_ui=5.0, est=4.676610963880016, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='1241', r_ui=3.0, est=3.306451885028324, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='1007', r_ui=4.0, est=4.07299129871518, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='411', r_ui=4.0, est=3.095287351974516, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='153', r_ui=5.0, est=3.906309635290134, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='13', r_ui=2.0, est=3.0900705467272784, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='762', r_ui=3.0, est=3.2968713502417457, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='173', r_ui=2.0, est=3.487360066550778, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='1022', r_ui=4.0, est=3.7526838857752236, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='845', r_ui=4.0, est=3.4429348024311275, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='269', r_ui=3.0, est=3.598182140750236, details={'was_impossible': False}),\n",
       " Prediction(uid='196', iid='110', r_ui=1.0, est=2.404172446127014, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='302', r_ui=3.0, est=3.6725618587533475, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='566', r_ui=5.0, est=3.865757603879957, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='250', r_ui=1.0, est=2.693476098916135, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='148', r_ui=4.0, est=3.590002291386284, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='263', r_ui=3.0, est=2.6635918044809053, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='470', r_ui=5.0, est=4.069603479097951, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='983', r_ui=3.0, est=2.930919996958474, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='281', r_ui=4.0, est=3.707858223395038, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='385', r_ui=4.0, est=3.6167587048810015, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='588', r_ui=4.0, est=3.914617430186783, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='406', r_ui=1.0, est=1.9772446301131312, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='925', r_ui=5.0, est=4.004658302413054, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='977', r_ui=3.0, est=2.919553031584158, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='322', r_ui=5.0, est=3.899039110197165, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='53', r_ui=1.0, est=1.8568696957016653, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='333', r_ui=3.0, est=3.276484261286493, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='591', r_ui=4.0, est=3.603739204148172, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='742', r_ui=3.0, est=3.8510800458909373, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='770', r_ui=2.0, est=3.148129703772001, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='550', r_ui=4.0, est=3.6680548719198938, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='237', r_ui=2.0, est=3.586201071937489, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1277', r_ui=4.0, est=3.845804501352694, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1253', r_ui=4.0, est=3.3003951656893196, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='71', r_ui=5.0, est=4.40364771040829, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='554', r_ui=1.0, est=2.304218555265076, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='257', r_ui=4.0, est=3.7605474194391, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='44', r_ui=5.0, est=3.9191302515952358, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='117', r_ui=5.0, est=4.125859381479464, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='327', r_ui=3.0, est=3.603934040300941, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='288', r_ui=1.0, est=1.8996089464526806, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='225', r_ui=4.0, est=3.390752885346333, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='988', r_ui=4.0, est=3.166821916063177, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='31', r_ui=4.0, est=4.004621456545958, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='939', r_ui=5.0, est=4.10844343753547, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='546', r_ui=4.0, est=2.8985381774129326, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='100', r_ui=4.0, est=4.051690034810361, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='338', r_ui=3.0, est=2.6318586596978153, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='717', r_ui=3.0, est=3.2249803368596406, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='118', r_ui=2.0, est=3.0173538915888436, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='226', r_ui=5.0, est=3.9324999411886505, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='300', r_ui=5.0, est=4.360384752627061, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='299', r_ui=3.0, est=2.935926987932157, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='596', r_ui=4.0, est=3.469437175705542, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='95', r_ui=3.0, est=3.5780119274553766, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='243', r_ui=2.0, est=2.2128051969801383, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1016', r_ui=5.0, est=4.087872678831525, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='79', r_ui=5.0, est=4.020077458743423, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='306', r_ui=4.0, est=4.0114350754170625, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='106', r_ui=2.0, est=2.7808396703610803, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='829', r_ui=4.0, est=3.4326745604985343, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='934', r_ui=3.0, est=3.1131932605636834, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1399', r_ui=2.0, est=2.9852561867593015, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='754', r_ui=2.0, est=3.1076110163775255, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='595', r_ui=3.0, est=3.086520983064519, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='121', r_ui=2.0, est=3.3940832830174656, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='568', r_ui=4.0, est=3.6851472859079237, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='303', r_ui=3.0, est=3.694576229562766, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='332', r_ui=4.0, est=3.7829345206764673, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='540', r_ui=4.0, est=3.2023743953082615, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1046', r_ui=3.0, est=3.385248163777226, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='98', r_ui=5.0, est=4.647188793903643, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='56', r_ui=3.0, est=3.0653174075435206, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='880', r_ui=3.0, est=3.098562219962364, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='203', r_ui=5.0, est=4.252715670663872, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1336', r_ui=3.0, est=2.473998583147923, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1083', r_ui=1.0, est=2.2875125628804556, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='291', r_ui=4.0, est=3.7192541458773296, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='356', r_ui=5.0, est=3.883883120283981, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='684', r_ui=4.0, est=3.8755154714481455, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='38', r_ui=5.0, est=3.6553848709683026, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='477', r_ui=4.0, est=3.5492061505387844, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='258', r_ui=1.0, est=2.783657386389004, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='298', r_ui=3.0, est=3.570340139101372, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='820', r_ui=2.0, est=2.5649574072959034, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1033', r_ui=3.0, est=2.7995692849598317, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='887', r_ui=4.0, est=3.4008044398407455, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='330', r_ui=4.0, est=3.526872691738429, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='689', r_ui=4.0, est=3.4663025296205485, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='159', r_ui=5.0, est=3.8641144156625553, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='12', r_ui=1.0, est=3.4139890337145298, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='55', r_ui=4.0, est=3.5863016561693506, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='294', r_ui=3.0, est=3.06370548044676, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1213', r_ui=3.0, est=3.03342068983635, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1042', r_ui=5.0, est=3.7940330509095985, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='177', r_ui=4.0, est=3.870311527862781, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='1385', r_ui=2.0, est=2.821143922926299, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='331', r_ui=3.0, est=3.731974304268837, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='77', r_ui=5.0, est=3.990267787226403, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='405', r_ui=3.0, est=3.057731894288135, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='147', r_ui=4.0, est=3.7640288599674845, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='295', r_ui=2.0, est=2.8816244801717446, details={'was_impossible': False}),\n",
       " Prediction(uid='186', iid='269', r_ui=1.0, est=3.252777906330908, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='377', r_ui=1.0, est=2.1066512197492298, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='376', r_ui=3.0, est=2.9752979356876965, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='128', r_ui=5.0, est=3.850844280307773, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='80', r_ui=4.0, est=3.1963644391700896, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='241', r_ui=3.0, est=3.18265783169696, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='258', r_ui=5.0, est=4.560504377569869, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='510', r_ui=5.0, est=4.286385077316334, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='79', r_ui=4.0, est=4.3624380750199965, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='791', r_ui=1.0, est=2.3162452354958583, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='511', r_ui=4.0, est=4.152989249158326, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='227', r_ui=4.0, est=3.5803072327528773, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='433', r_ui=3.0, est=3.9148770382513702, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='173', r_ui=5.0, est=4.921151170616174, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='687', r_ui=1.0, est=1.4279985485881772, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='456', r_ui=1.0, est=1.8035125520994684, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='399', r_ui=4.0, est=3.351058424033924, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='186', r_ui=5.0, est=4.554885490366518, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='96', r_ui=5.0, est=4.36891242764713, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='294', r_ui=1.0, est=2.036417140189259, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='780', r_ui=1.0, est=2.291790522491618, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='29', r_ui=1.0, est=2.0715116780077247, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='117', r_ui=4.0, est=3.7630806110713757, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='683', r_ui=1.0, est=2.15006114627649, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='403', r_ui=5.0, est=3.8270921154282527, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='999', r_ui=4.0, est=3.229727707313033, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='502', r_ui=4.0, est=3.8792789322380945, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='435', r_ui=5.0, est=4.252435110123401, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='121', r_ui=3.0, est=3.4002311139266768, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='176', r_ui=5.0, est=4.327118895935814, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='222', r_ui=4.0, est=3.825274678467385, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='550', r_ui=5.0, est=3.7226892677817913, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='948', r_ui=1.0, est=1.6304373025555323, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='393', r_ui=4.0, est=3.414056157705418, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='110', r_ui=1.0, est=2.0053924271711, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='648', r_ui=4.0, est=3.7829019805774258, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='118', r_ui=4.0, est=3.104258280170966, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='692', r_ui=4.0, est=3.914352602496852, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='386', r_ui=3.0, est=2.875131462129142, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='226', r_ui=4.0, est=3.631005283854977, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='238', r_ui=5.0, est=4.09658873793877, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='554', r_ui=1.0, est=2.73042739028669, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='407', r_ui=3.0, est=2.4855631121280624, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='878', r_ui=1.0, est=2.0746943076796978, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='455', r_ui=5.0, est=3.5951697840438546, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='358', r_ui=5.0, est=3.2944002658828713, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='208', r_ui=5.0, est=4.711112275176339, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='172', r_ui=4.0, est=4.895845995924084, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='230', r_ui=4.0, est=3.9263674661244883, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='997', r_ui=1.0, est=1.7080181911466965, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='1001', r_ui=1.0, est=1.7054708210289733, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='153', r_ui=5.0, est=4.582356541860514, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='154', r_ui=4.0, est=4.136984093405807, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='194', r_ui=5.0, est=4.435365845296203, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='195', r_ui=4.0, est=4.173775993027584, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='411', r_ui=1.0, est=1.9082343357123714, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='168', r_ui=5.0, est=4.578245614224427, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='204', r_ui=5.0, est=4.168609248846999, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='871', r_ui=3.0, est=2.2741539750046966, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='651', r_ui=4.0, est=4.379281589148297, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='665', r_ui=1.0, est=2.0846270678250245, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='187', r_ui=5.0, est=4.516123306934755, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='53', r_ui=3.0, est=3.4122795657850107, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='515', r_ui=5.0, est=4.0797136050773775, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='85', r_ui=5.0, est=3.7515010445721497, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='996', r_ui=1.0, est=1.9603276514232197, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='451', r_ui=4.0, est=3.5347317170754367, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='840', r_ui=4.0, est=3.0141068262602846, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='932', r_ui=1.0, est=1.854666751183731, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='167', r_ui=3.0, est=3.1774614157160506, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='862', r_ui=1.0, est=1.6194252206940587, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='105', r_ui=1.0, est=1.7098844282697523, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='431', r_ui=4.0, est=4.139279463994876, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='231', r_ui=2.0, est=2.586109832556355, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='367', r_ui=1.0, est=2.745208837420697, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='449', r_ui=1.0, est=2.0684786360282597, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='202', r_ui=5.0, est=4.251845417682363, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='216', r_ui=4.0, est=3.878718643427851, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='988', r_ui=1.0, est=1.7388143421556106, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='184', r_ui=5.0, est=3.798438894231099, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='1003', r_ui=1.0, est=2.465143927286111, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='211', r_ui=3.0, est=3.539133787053216, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='94', r_ui=3.0, est=3.1743206913472672, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='175', r_ui=4.0, est=4.212497819863552, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='636', r_ui=3.0, est=3.220043591205686, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='24', r_ui=5.0, est=3.8892620398702826, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='684', r_ui=3.0, est=3.480031012754638, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='229', r_ui=2.0, est=2.837759202936203, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='546', r_ui=3.0, est=3.159633544063037, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='163', r_ui=1.0, est=2.94500084332325, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='109', r_ui=4.0, est=4.008818626732422, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='523', r_ui=5.0, est=4.0833483954743555, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='21', r_ui=4.0, est=2.972390072442068, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='1002', r_ui=1.0, est=1.9726966708368237, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='201', r_ui=4.0, est=3.3384787682513553, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='568', r_ui=4.0, est=3.43899789335549, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='181', r_ui=5.0, est=5, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='17', r_ui=4.0, est=3.392609992300664, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='1000', r_ui=3.0, est=3.0684056854870074, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='566', r_ui=3.0, est=3.142974863289683, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='144', r_ui=5.0, est=4.843854811322019, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='2', r_ui=2.0, est=2.4859129865516087, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='161', r_ui=4.0, est=3.321123118809337, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='688', r_ui=1.0, est=1.3168135919649568, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='712', r_ui=4.0, est=3.193874869822897, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='384', r_ui=3.0, est=2.8227827163478203, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='290', r_ui=5.0, est=3.7293557503425445, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='430', r_ui=4.0, est=3.91510669069615, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='210', r_ui=3.0, est=4.055240825335485, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='89', r_ui=5.0, est=3.929637702556669, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='228', r_ui=4.0, est=4.184001798485481, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='732', r_ui=4.0, est=4.052000876477512, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='4', r_ui=5.0, est=4.3951837122957045, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='127', r_ui=5.0, est=4.609382502869887, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='926', r_ui=1.0, est=2.086796262132861, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='62', r_ui=4.0, est=3.2295005215971777, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='250', r_ui=5.0, est=4.658668592811326, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='405', r_ui=1.0, est=2.4401783866013282, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='50', r_ui=5.0, est=5, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='209', r_ui=4.0, est=3.992031960322635, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='526', r_ui=4.0, est=3.423646319982479, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='174', r_ui=5.0, est=4.949137041730745, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='998', r_ui=1.0, est=1.6859594068934252, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='731', r_ui=3.0, est=2.857734268479472, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='385', r_ui=4.0, est=3.6025543411960497, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='265', r_ui=3.0, est=3.7444846857485974, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='233', r_ui=3.0, est=3.2023792074355755, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='792', r_ui=4.0, est=3.8937645434427464, details={'was_impossible': False}),\n",
       " Prediction(uid='22', iid='68', r_ui=4.0, est=3.4916026332630095, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='51', r_ui=2.0, est=3.1606409895161827, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='815', r_ui=4.0, est=3.2382566748238855, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='756', r_ui=2.0, est=2.796336344587072, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='673', r_ui=3.0, est=3.606864769508997, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='186', r_ui=3.0, est=3.912746377207471, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='265', r_ui=4.0, est=3.366438543839016, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='17', r_ui=2.0, est=3.16181691600123, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='381', r_ui=4.0, est=3.8063761944405026, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='707', r_ui=4.0, est=4.0792420576813715, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='550', r_ui=1.0, est=2.6148395396350557, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='183', r_ui=4.0, est=4.1515496028821195, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='310', r_ui=3.0, est=3.1121440974107317, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='172', r_ui=4.0, est=4.422762168051686, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='790', r_ui=4.0, est=3.4736456174190926, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='53', r_ui=3.0, est=3.5515222682864263, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='154', r_ui=5.0, est=4.553924906746864, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='662', r_ui=3.0, est=3.6315910729096865, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='148', r_ui=2.0, est=2.927921471272884, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='409', r_ui=4.0, est=3.0825827465697384, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='89', r_ui=5.0, est=4.584295668469056, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='380', r_ui=4.0, est=3.4570051316324983, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='167', r_ui=3.0, est=2.921304384936121, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='652', r_ui=5.0, est=4.46227692869068, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='155', r_ui=3.0, est=2.9285013635949255, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='7', r_ui=4.0, est=4.341262239430645, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='216', r_ui=4.0, est=4.063076263909847, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='31', r_ui=4.0, est=3.5541548112311108, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='220', r_ui=2.0, est=3.0955827701278236, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='238', r_ui=5.0, est=4.590426885155896, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='676', r_ui=4.0, est=3.8160421930877657, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='100', r_ui=4.0, est=4.366845830955296, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='97', r_ui=2.0, est=3.252858128756473, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='743', r_ui=5.0, est=2.954478540217927, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='369', r_ui=4.0, est=2.9508289666996887, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='237', r_ui=5.0, est=4.057833680812205, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='95', r_ui=4.0, est=3.668876150990786, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='509', r_ui=5.0, est=4.363564135510126, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='157', r_ui=4.0, est=3.913346151160475, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='278', r_ui=3.0, est=2.8989814923808304, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='428', r_ui=4.0, est=4.208576264834947, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='13', r_ui=4.0, est=3.6995900578789787, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='596', r_ui=4.0, est=3.369138667571754, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1225', r_ui=2.0, est=2.7776224439807717, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='712', r_ui=3.0, est=3.368494655364237, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='101', r_ui=5.0, est=3.895202946274637, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1017', r_ui=4.0, est=3.5554260348446873, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='324', r_ui=4.0, est=3.8220692298678287, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='179', r_ui=5.0, est=4.719381442810407, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='226', r_ui=1.0, est=2.7233638324650484, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1178', r_ui=3.0, est=3.0070731919808966, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='54', r_ui=2.0, est=2.8160088439769813, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='747', r_ui=4.0, est=3.7908058637974844, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='208', r_ui=5.0, est=4.5335340313942, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1098', r_ui=5.0, est=4.576126957562985, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='818', r_ui=2.0, est=2.941261097450651, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='90', r_ui=4.0, est=3.558545655243133, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='762', r_ui=3.0, est=3.548541528026577, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='232', r_ui=4.0, est=3.4075317925267474, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='20', r_ui=4.0, est=3.8741521147098115, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='764', r_ui=5.0, est=3.303070583371488, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='22', r_ui=4.0, est=3.9677841447633018, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='287', r_ui=3.0, est=3.5023095559712707, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='122', r_ui=4.0, est=3.2014093253662645, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='62', r_ui=2.0, est=2.783358027135235, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='508', r_ui=4.0, est=4.416794899980465, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='240', r_ui=3.0, est=3.2043339024311273, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='411', r_ui=4.0, est=3.5653142231820616, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='180', r_ui=4.0, est=4.483082492054042, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='191', r_ui=5.0, est=4.6595326696163735, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1045', r_ui=5.0, est=4.0033590563388755, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='168', r_ui=5.0, est=4.8193302009932975, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='953', r_ui=4.0, est=3.8211017827984155, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='164', r_ui=3.0, est=3.319108844041895, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='258', r_ui=5.0, est=4.381633713090822, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1107', r_ui=2.0, est=3.049376103073329, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='294', r_ui=4.0, est=2.67250429641694, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='204', r_ui=4.0, est=3.733137697998685, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1039', r_ui=4.0, est=4.530551718307599, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='196', r_ui=5.0, est=4.539845285051745, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1074', r_ui=4.0, est=3.3332565460043972, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='181', r_ui=4.0, est=3.9065315999282517, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='886', r_ui=5.0, est=3.7879084791646176, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='475', r_ui=4.0, est=4.879587493705479, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='117', r_ui=2.0, est=3.0374991216056593, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='217', r_ui=5.0, est=3.999444838592146, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='723', r_ui=3.0, est=3.4447093860765907, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='135', r_ui=4.0, est=3.9867404231487185, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='290', r_ui=3.0, est=3.1440293015645002, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='72', r_ui=4.0, est=3.2771733424983345, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='209', r_ui=4.0, est=4.413735475995684, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='554', r_ui=3.0, est=2.879025488419204, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='631', r_ui=4.0, est=4.017818730664659, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='69', r_ui=4.0, est=3.1763247254237417, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='367', r_ui=1.0, est=3.4342175782248123, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='724', r_ui=4.0, est=3.8344196210675734, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1047', r_ui=2.0, est=2.327011250744869, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='950', r_ui=1.0, est=2.889716243835703, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='365', r_ui=2.0, est=2.8573076680392946, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='955', r_ui=4.0, est=3.5792495256987014, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='151', r_ui=5.0, est=4.341238549115468, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='559', r_ui=4.0, est=3.8950023159853218, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='926', r_ui=2.0, est=2.191569005551319, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1048', r_ui=4.0, est=3.564603743975602, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='161', r_ui=4.0, est=3.2075484502366307, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1054', r_ui=3.0, est=2.7525233790399097, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='255', r_ui=2.0, est=3.0155917816911986, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='456', r_ui=3.0, est=2.5702910395075866, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='584', r_ui=5.0, est=4.188704549814374, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='738', r_ui=4.0, est=3.311445424591752, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='77', r_ui=4.0, est=3.160169094064358, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='42', r_ui=5.0, est=4.431026732876685, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='866', r_ui=5.0, est=3.237533419704915, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='52', r_ui=4.0, est=4.121285256609865, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='685', r_ui=2.0, est=3.0368096125052713, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1209', r_ui=3.0, est=2.745387657806933, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='301', r_ui=2.0, est=3.1743449483914237, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='145', r_ui=3.0, est=2.717698048406255, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='566', r_ui=4.0, est=3.3221839443836405, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='40', r_ui=2.0, est=2.8631177170774036, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='739', r_ui=3.0, est=3.075097751632841, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='628', r_ui=4.0, est=3.9003447398421147, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='856', r_ui=5.0, est=4.333986797478233, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='959', r_ui=4.0, est=4.074308423182804, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='471', r_ui=1.0, est=3.0244474823871004, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='410', r_ui=4.0, est=3.717454584206201, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='451', r_ui=4.0, est=3.586009160347564, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='32', r_ui=2.0, est=3.7877294463602347, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='92', r_ui=4.0, est=3.9154691526322223, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='86', r_ui=4.0, est=4.339332629332812, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='581', r_ui=4.0, est=3.723781066519465, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='66', r_ui=4.0, est=3.565759807714053, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='200', r_ui=5.0, est=4.33320919758827, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='111', r_ui=4.0, est=3.451633059201468, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='537', r_ui=5.0, est=4.151183012832248, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='281', r_ui=3.0, est=3.0693669248188815, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='833', r_ui=3.0, est=3.189751649185013, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='553', r_ui=5.0, est=3.583017358276117, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='946', r_ui=4.0, est=3.280293056489757, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='721', r_ui=5.0, est=4.047475491502316, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='660', r_ui=4.0, est=3.9322709033887064, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='780', r_ui=4.0, est=3.468280303489878, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='215', r_ui=4.0, est=3.9219638869395053, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='732', r_ui=1.0, est=2.95872342595814, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='521', r_ui=4.0, est=4.26471859152501, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='941', r_ui=4.0, est=3.646358460727273, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1079', r_ui=2.0, est=2.6510532199648056, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='105', r_ui=2.0, est=2.223508567907719, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='746', r_ui=3.0, est=3.888078912946592, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='173', r_ui=4.0, est=4.699585133031531, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='458', r_ui=3.0, est=3.5882344527227317, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1132', r_ui=4.0, est=3.266802881632174, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='162', r_ui=4.0, est=4.0114986472211775, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='655', r_ui=5.0, est=4.3307000289617275, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='246', r_ui=5.0, est=4.66952599816276, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='64', r_ui=5.0, est=4.662405630531405, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='174', r_ui=3.0, est=3.77542645087543, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='318', r_ui=5.0, est=4.769231029004744, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='754', r_ui=4.0, est=3.5350968552810307, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='156', r_ui=4.0, est=4.245260020497695, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='268', r_ui=5.0, est=4.306589691680071, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='3', r_ui=5.0, est=3.763892263945631, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1057', r_ui=4.0, est=3.035625266346459, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='401', r_ui=3.0, est=3.0075715267133623, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='716', r_ui=3.0, est=3.0837003624133144, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1168', r_ui=4.0, est=3.705110954522404, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='468', r_ui=1.0, est=3.2613649057148675, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='772', r_ui=4.0, est=3.5877707209596625, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='50', r_ui=5.0, est=4.431074362537197, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='357', r_ui=5.0, est=4.884421479212887, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='82', r_ui=3.0, est=3.398041228053401, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='197', r_ui=4.0, est=4.477379452248909, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='527', r_ui=5.0, est=4.243104791466434, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='393', r_ui=3.0, est=3.101815252287226, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='169', r_ui=5.0, est=4.813684306310661, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='763', r_ui=4.0, est=3.7054483793481547, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='222', r_ui=2.0, est=3.0175310461811655, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='317', r_ui=5.0, est=4.51923913564944, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='629', r_ui=4.0, est=3.520475204704405, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='697', r_ui=4.0, est=3.8586590619943397, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='71', r_ui=4.0, est=3.633120367263243, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1109', r_ui=4.0, est=3.5902296610245306, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='949', r_ui=4.0, est=3.493746697991692, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='235', r_ui=1.0, est=2.7898040299742313, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1188', r_ui=4.0, est=3.194977371326829, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='80', r_ui=3.0, est=2.8184351014009077, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='433', r_ui=5.0, est=4.402520497750599, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='68', r_ui=5.0, est=3.744981114749243, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='70', r_ui=4.0, est=4.226650260206002, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='241', r_ui=4.0, est=3.8786294094068974, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='126', r_ui=4.0, est=4.1800781833465654, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='26', r_ui=5.0, est=3.9528695449073856, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1', r_ui=4.0, est=3.3628137382486463, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1136', r_ui=3.0, est=3.3392565613068914, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='158', r_ui=3.0, est=2.835621946482378, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='871', r_ui=3.0, est=2.497099231301563, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1119', r_ui=5.0, est=4.0078378232926966, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1095', r_ui=2.0, est=2.5514456027225014, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='609', r_ui=3.0, est=3.429631735197413, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='710', r_ui=3.0, est=3.7472877309287322, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='144', r_ui=1.0, est=3.0835139470743127, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='9', r_ui=5.0, est=5, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='109', r_ui=4.0, est=3.0886997650161407, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1118', r_ui=4.0, est=3.693187960935399, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='118', r_ui=2.0, est=2.127118023600704, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1041', r_ui=4.0, est=3.4125108280875596, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='708', r_ui=4.0, est=4.102138025923426, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1053', r_ui=2.0, est=3.2821783344534676, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1150', r_ui=4.0, est=3.7345002191107133, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='153', r_ui=4.0, est=3.767440983300202, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='114', r_ui=4.0, est=4.995798040220863, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='214', r_ui=5.0, est=4.263466917640533, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1467', r_ui=5.0, est=3.9617136079661432, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='249', r_ui=4.0, est=3.782735057472572, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='234', r_ui=3.0, est=3.622565662007265, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='845', r_ui=3.0, est=3.4556716912383756, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1028', r_ui=3.0, est=2.9907574673831694, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='58', r_ui=3.0, est=3.976741590488118, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='171', r_ui=5.0, est=4.427993767020777, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='651', r_ui=4.0, est=4.215291190695922, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='276', r_ui=5.0, est=4.850806046645398, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='528', r_ui=3.0, est=4.1834480460208745, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='28', r_ui=4.0, est=3.9309110556819, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='744', r_ui=3.0, est=3.5840312736700906, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='65', r_ui=4.0, est=3.8488354584317093, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='291', r_ui=2.0, est=3.199791894337415, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='924', r_ui=4.0, est=3.7341452163779936, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1428', r_ui=4.0, est=3.837882733286176, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='188', r_ui=4.0, est=3.6951472179261575, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='193', r_ui=4.0, est=3.9438826156427234, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='1012', r_ui=2.0, est=3.1988515351054807, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='56', r_ui=5.0, est=5, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='383', r_ui=3.0, est=2.4838824822342325, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='88', r_ui=4.0, est=3.5670121924554583, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='735', r_ui=5.0, est=4.246969022171116, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='121', r_ui=1.0, est=2.0380695078540656, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='455', r_ui=2.0, est=3.111073225111934, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='67', r_ui=4.0, est=3.1398749233809036, details={'was_impossible': False}),\n",
       " Prediction(uid='244', iid='650', r_ui=3.0, est=3.842266613707659, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='346', r_ui=1.0, est=3.0346994363711204, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='328', r_ui=5.0, est=4.407758751692031, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='322', r_ui=5.0, est=3.857694168162782, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='288', r_ui=3.0, est=2.9041286299071487, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='258', r_ui=4.0, est=4.038347167145804, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='343', r_ui=4.0, est=3.5387447246178825, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='300', r_ui=5.0, est=4.8769378602563656, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='894', r_ui=4.0, est=2.814486443891954, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='323', r_ui=5.0, est=3.988603966090351, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='748', r_ui=2.0, est=3.287783172797418, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='751', r_ui=4.0, est=3.703057292860472, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='984', r_ui=5.0, est=3.616058069674338, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='294', r_ui=3.0, est=3.5085507510215397, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='286', r_ui=1.0, est=3.1197745707787155, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='243', r_ui=3.0, est=2.9120120409804082, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='347', r_ui=5.0, est=4.156072964803322, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='313', r_ui=5.0, est=4.769171856547419, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='688', r_ui=3.0, est=2.517553604103759, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='315', r_ui=3.0, est=3.8812460161721374, details={'was_impossible': False}),\n",
       " Prediction(uid='166', iid='687', r_ui=1.0, est=2.023712250421903, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='474', r_ui=4.0, est=4.186792146032436, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='317', r_ui=4.0, est=4.197485970199997, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='281', r_ui=3.0, est=3.4064571745454164, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='486', r_ui=3.0, est=3.936748930932586, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='181', r_ui=4.0, est=4.471357915288569, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='625', r_ui=4.0, est=3.6714995434650897, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='1346', r_ui=3.0, est=3.3544534499920093, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='252', r_ui=4.0, est=3.3477501475806246, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='152', r_ui=3.0, est=3.665900632821195, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='91', r_ui=2.0, est=3.3222357626934294, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='8', r_ui=5.0, est=4.331491864868988, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='842', r_ui=4.0, est=3.5387105928655607, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='477', r_ui=4.0, est=3.32386537798349, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='261', r_ui=4.0, est=3.131796748774322, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='432', r_ui=4.0, est=3.94849033915854, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='151', r_ui=3.0, est=3.3432979531354623, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='98', r_ui=4.0, est=4.513550199744472, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='418', r_ui=4.0, est=4.049791109531808, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='465', r_ui=4.0, est=3.659622294498719, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='1142', r_ui=4.0, est=4.140265067443441, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='660', r_ui=3.0, est=3.723948721665284, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='652', r_ui=3.0, est=3.677957260347152, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='172', r_ui=4.0, est=4.626197285308128, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='498', r_ui=5.0, est=4.668951888926539, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='144', r_ui=4.0, est=4.174844084176083, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='195', r_ui=4.0, est=4.5366746493885275, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='496', r_ui=5.0, est=4.6083529665807585, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='237', r_ui=5.0, est=4.028774914231187, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='200', r_ui=3.0, est=3.845800295942753, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='473', r_ui=3.0, est=3.314820615865375, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='286', r_ui=4.0, est=3.585444799482083, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='502', r_ui=5.0, est=3.8412877165916988, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='311', r_ui=3.0, est=3.8261770220743805, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='651', r_ui=5.0, est=4.515115689195625, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='993', r_ui=4.0, est=3.7157688060555736, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='69', r_ui=4.0, est=4.377260086931402, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='71', r_ui=5.0, est=4.505821251899715, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='197', r_ui=4.0, est=4.150802648636574, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='213', r_ui=3.0, est=3.942636052716943, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='28', r_ui=4.0, est=4.256424969164574, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='507', r_ui=4.0, est=4.084592317991735, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='274', r_ui=3.0, est=3.6736553623248254, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='202', r_ui=3.0, est=3.8843433208632456, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='185', r_ui=3.0, est=3.742430928376802, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='503', r_ui=4.0, est=3.891679420033063, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='178', r_ui=5.0, est=4.449402036213635, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='203', r_ui=3.0, est=3.6112806993859436, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='596', r_ui=3.0, est=3.5748377536033353, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='99', r_ui=3.0, est=3.816898473959004, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='511', r_ui=4.0, est=4.479366005800506, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='471', r_ui=4.0, est=3.785740017705798, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='183', r_ui=3.0, est=3.8595431846649872, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='864', r_ui=3.0, est=3.3780126984462346, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='483', r_ui=5.0, est=4.671777089118721, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='705', r_ui=4.0, est=4.2817284778616145, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='527', r_ui=5.0, est=4.431369410309853, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='194', r_ui=5.0, est=4.314990225818639, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='294', r_ui=3.0, est=3.5145300771055314, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='58', r_ui=4.0, est=3.8147083350337168, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='430', r_ui=5.0, est=4.44987654031605, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='134', r_ui=5.0, est=4.585912763211956, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='23', r_ui=4.0, est=4.113353119962945, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='318', r_ui=5.0, est=4.7675036590613695, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='1', r_ui=5.0, est=4.356112350073882, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='79', r_ui=5.0, est=4.645092387698705, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='257', r_ui=4.0, est=4.067376242059165, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='133', r_ui=3.0, est=4.177418217009563, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='118', r_ui=4.0, est=3.910856458006471, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='97', r_ui=4.0, est=4.273022433980525, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='514', r_ui=4.0, est=4.12565117864577, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='588', r_ui=4.0, est=4.151076292153592, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='530', r_ui=5.0, est=4.402502687535432, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='603', r_ui=5.0, est=4.516090865301686, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='127', r_ui=5.0, est=4.694047765225412, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='186', r_ui=4.0, est=4.342525170259031, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='435', r_ui=5.0, est=4.274318730168437, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='951', r_ui=4.0, est=3.481946174348819, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='22', r_ui=4.0, est=4.541189134289598, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='866', r_ui=3.0, est=3.216621105254813, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='205', r_ui=5.0, est=4.292201720021554, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='393', r_ui=4.0, est=3.7227051577645818, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='143', r_ui=5.0, est=4.436500721398832, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='168', r_ui=5.0, est=4.495144803095512, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='946', r_ui=3.0, est=3.44858179441308, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='604', r_ui=5.0, est=4.350805001048927, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='153', r_ui=3.0, est=3.8711018901762726, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='484', r_ui=4.0, est=4.2466713801582285, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='211', r_ui=5.0, est=4.187089350427144, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='423', r_ui=5.0, est=4.394583114760194, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='208', r_ui=5.0, est=4.148986115552476, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='523', r_ui=4.0, est=4.298935203708353, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='88', r_ui=5.0, est=4.108163589764392, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='196', r_ui=4.0, est=3.9057517620768727, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='284', r_ui=4.0, est=3.6660033962435152, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='504', r_ui=3.0, est=3.775187706982343, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='193', r_ui=5.0, est=4.262965726899691, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='265', r_ui=4.0, est=4.442338268608036, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='215', r_ui=5.0, est=4.208043158469231, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='276', r_ui=2.0, est=3.447463482770149, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='419', r_ui=5.0, est=4.295611127395605, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='820', r_ui=4.0, est=3.1385967494985136, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='132', r_ui=5.0, est=4.47981776336113, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='479', r_ui=5.0, est=4.362110338508198, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='210', r_ui=5.0, est=4.531137298046189, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='333', r_ui=5.0, est=4.254904214721553, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='526', r_ui=5.0, est=4.039288792924052, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='199', r_ui=4.0, est=4.308651848531484, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='174', r_ui=5.0, est=4.769381729379087, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='50', r_ui=5.0, est=4.784174242616485, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='121', r_ui=4.0, est=4.049259001823548, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='427', r_ui=5.0, est=4.542179783340975, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='546', r_ui=3.0, est=3.4150452426135463, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='845', r_ui=3.0, est=3.3835026475968317, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='125', r_ui=3.0, est=3.7434454841244205, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='549', r_ui=4.0, est=3.7819496269878345, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='204', r_ui=4.0, est=4.398871586843162, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='9', r_ui=4.0, est=4.057726984579253, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='357', r_ui=5.0, est=4.508008285851893, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='187', r_ui=5.0, est=4.731752844469382, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='356', r_ui=3.0, est=3.443866430604247, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='742', r_ui=3.0, est=3.806313118010156, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='275', r_ui=3.0, est=4.135109443452292, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='485', r_ui=3.0, est=3.9351494305245946, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='402', r_ui=3.0, est=3.574007841502131, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='282', r_ui=4.0, est=4.161717739893411, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='679', r_ui=3.0, est=3.308354056502093, details={'was_impossible': False}),\n",
       " Prediction(uid='298', iid='482', r_ui=5.0, est=4.2583393956764315, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='265', r_ui=2.0, est=3.470527894535474, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='20', r_ui=3.0, est=3.274727058401975, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='1067', r_ui=4.0, est=3.7815438699197657, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='8', r_ui=5.0, est=4.1660918044241795, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='127', r_ui=5.0, est=4.562753982004958, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='92', r_ui=4.0, est=3.9815913818271866, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='228', r_ui=4.0, est=3.971927916733123, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='234', r_ui=5.0, est=3.9082747142355125, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='11', r_ui=4.0, est=4.013532728186398, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='762', r_ui=4.0, est=3.7225963183831343, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='69', r_ui=1.0, est=2.765266272038451, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='530', r_ui=5.0, est=4.259879944099058, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='462', r_ui=4.0, est=4.013208983668823, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='172', r_ui=4.0, est=4.269534664773115, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='466', r_ui=5.0, est=4.191976648253563, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='511', r_ui=5.0, est=4.7097120819855025, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='642', r_ui=5.0, est=4.210747818426552, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='763', r_ui=2.0, est=3.2071849089732356, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='32', r_ui=5.0, est=4.429163595144867, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='443', r_ui=4.0, est=4.111696269928169, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='543', r_ui=2.0, est=3.4189122216658143, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='82', r_ui=4.0, est=3.734474151964367, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='475', r_ui=5.0, est=4.437196273335773, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='89', r_ui=5.0, est=4.720540376796206, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='310', r_ui=3.0, est=3.0090619772750578, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='12', r_ui=5.0, est=4.713940680604327, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='470', r_ui=2.0, est=3.3137328707574736, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='471', r_ui=2.0, est=3.318900809562905, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='187', r_ui=5.0, est=4.498677446856421, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='969', r_ui=1.0, est=2.9077138912261558, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='496', r_ui=1.0, est=3.3455842709932764, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='93', r_ui=3.0, est=4.154178039655656, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='1008', r_ui=5.0, est=4.066413457184441, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='181', r_ui=4.0, est=3.82718082856036, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='1073', r_ui=5.0, est=4.361748060963005, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='952', r_ui=5.0, est=3.928652369139897, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='9', r_ui=5.0, est=4.767016842249065, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='431', r_ui=4.0, est=3.5259625824791967, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='50', r_ui=5.0, est=4.253838170347397, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='178', r_ui=5.0, est=4.650608577143568, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='77', r_ui=2.0, est=2.722535611847286, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='269', r_ui=3.0, est=3.848109936200444, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='22', r_ui=3.0, est=3.662869251064845, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='237', r_ui=2.0, est=3.351963637684803, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='596', r_ui=1.0, est=2.7486538791620467, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='7', r_ui=5.0, est=4.664335080314461, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='121', r_ui=3.0, est=2.3602700310071185, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='183', r_ui=5.0, est=4.448666830009416, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='4', r_ui=4.0, est=3.8263591428961847, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='357', r_ui=5.0, est=4.587424470069453, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='33', r_ui=4.0, est=3.474369635455949, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='922', r_ui=3.0, est=3.977374175714231, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='96', r_ui=3.0, est=3.6433763910239363, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='56', r_ui=5.0, est=4.695812979818898, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='273', r_ui=4.0, est=3.7131666022665066, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='177', r_ui=5.0, est=4.456885862087691, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='23', r_ui=5.0, est=4.716384851676393, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='174', r_ui=5.0, est=3.9600101723655636, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='673', r_ui=3.0, est=3.427855130396547, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='98', r_ui=3.0, est=4.273700339662019, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='847', r_ui=4.0, est=4.041872972770335, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='657', r_ui=3.0, est=4.275636052505446, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='13', r_ui=5.0, est=4.334378453895123, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='240', r_ui=5.0, est=4.00045512707136, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='124', r_ui=5.0, est=4.536152810091245, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='137', r_ui=5.0, est=4.437566449221559, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='654', r_ui=5.0, est=4.748508536971226, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='479', r_ui=5.0, est=4.737219022213428, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='176', r_ui=5.0, est=3.9733160785504342, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='317', r_ui=5.0, est=4.92872746174311, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='980', r_ui=4.0, est=3.5739764080671046, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='229', r_ui=3.0, est=2.900982205140253, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='279', r_ui=3.0, est=3.3377372990182055, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='282', r_ui=4.0, est=3.465606570072251, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='48', r_ui=5.0, est=4.694472431386464, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='284', r_ui=2.0, est=3.1199661561264604, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='741', r_ui=3.0, est=3.6013109452087044, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='684', r_ui=3.0, est=3.4107650145249457, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='772', r_ui=4.0, est=3.831266320946663, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='79', r_ui=4.0, est=3.672129512000278, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='644', r_ui=3.0, est=3.7918632151769534, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='185', r_ui=5.0, est=4.687332189481173, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='192', r_ui=5.0, est=4.424792575065848, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='218', r_ui=3.0, est=3.4780676393011465, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='302', r_ui=4.0, est=4.407168678693381, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='628', r_ui=5.0, est=4.075913738731696, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='83', r_ui=3.0, est=3.799363180544011, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='100', r_ui=5.0, est=4.9786533359874925, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='696', r_ui=4.0, est=3.650841758747517, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='117', r_ui=4.0, est=3.872623252901277, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='558', r_ui=5.0, est=4.172060333484884, details={'was_impossible': False}),\n",
       " Prediction(uid='115', iid='508', r_ui=5.0, est=4.218574125955139, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='465', r_ui=5.0, est=4.0311021264167755, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='259', r_ui=2.0, est=2.725824647958534, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='97', r_ui=4.0, est=4.283800962049515, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='746', r_ui=3.0, est=3.8733926320336036, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='510', r_ui=5.0, est=4.343440147064839, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='216', r_ui=4.0, est=4.104158644001979, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='50', r_ui=4.0, est=4.600038157363482, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='183', r_ui=5.0, est=4.334380362508293, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='203', r_ui=4.0, est=3.822449731848487, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='747', r_ui=3.0, est=3.261419020072152, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='483', r_ui=5.0, est=4.6079596184348155, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='210', r_ui=4.0, est=4.210403691746331, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='198', r_ui=5.0, est=4.26084232564859, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='568', r_ui=4.0, est=3.798763413541558, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='294', r_ui=4.0, est=3.4853743771462895, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='566', r_ui=4.0, est=3.988494308951231, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='237', r_ui=4.0, est=4.139598865222079, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='188', r_ui=4.0, est=3.791610377479584, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='127', r_ui=5.0, est=4.402875040917023, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='647', r_ui=3.0, est=3.9166361667405027, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='173', r_ui=5.0, est=4.417637508705299, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='175', r_ui=2.0, est=3.5857880057885003, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='527', r_ui=5.0, est=4.576726275796528, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='282', r_ui=4.0, est=3.9872759656483923, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='742', r_ui=4.0, est=4.031296393041043, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='298', r_ui=3.0, est=3.694474122879276, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='117', r_ui=5.0, est=4.276354288873876, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='806', r_ui=4.0, est=3.735707420071442, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='95', r_ui=4.0, est=4.241739102930594, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='448', r_ui=2.0, est=3.5492768762526916, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='83', r_ui=4.0, est=4.277369108393529, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='87', r_ui=5.0, est=4.216962952959817, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='705', r_ui=5.0, est=4.064071406969845, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='487', r_ui=4.0, est=4.245909072077634, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='243', r_ui=2.0, est=2.8284985739056214, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='64', r_ui=5.0, est=4.8432275699508756, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='496', r_ui=5.0, est=4.756055235641466, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='89', r_ui=4.0, est=4.235291839855953, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='79', r_ui=5.0, est=4.640829933440959, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='333', r_ui=2.0, est=3.362142784002237, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='98', r_ui=5.0, est=4.406827349481118, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='273', r_ui=3.0, est=3.7325792652326624, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='328', r_ui=4.0, est=3.8269280858518027, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='156', r_ui=3.0, est=3.551633818389147, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='732', r_ui=4.0, est=4.025202765968342, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='523', r_ui=4.0, est=4.112412334096744, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='182', r_ui=3.0, est=3.6487786677126772, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='56', r_ui=3.0, est=3.578805271752482, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='588', r_ui=5.0, est=4.168497177561612, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='22', r_ui=5.0, est=4.530787773900094, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='331', r_ui=3.0, est=3.6235202885495346, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='1016', r_ui=3.0, est=3.9443990635987998, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='494', r_ui=5.0, est=4.33490933320383, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='12', r_ui=5.0, est=4.545266035996327, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='202', r_ui=5.0, est=4.3448271277253605, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='300', r_ui=4.0, est=4.162390916138942, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='8', r_ui=4.0, est=4.179046309271102, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='100', r_ui=4.0, est=4.051884638087059, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='343', r_ui=4.0, est=3.4472219590416495, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='685', r_ui=2.0, est=3.362295608461795, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='15', r_ui=4.0, est=4.014115994579033, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='591', r_ui=3.0, est=3.732566831157699, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='689', r_ui=5.0, est=3.7657668025518656, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='485', r_ui=5.0, est=3.948628479254905, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='679', r_ui=3.0, est=3.170251705590766, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='895', r_ui=4.0, est=3.7554685733096687, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='220', r_ui=4.0, est=3.579854618635759, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='190', r_ui=5.0, est=4.351904125342092, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='96', r_ui=5.0, est=4.4005983405127305, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='125', r_ui=3.0, est=3.754155305224297, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='81', r_ui=4.0, est=3.6945144032538684, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='222', r_ui=4.0, est=4.062828665388491, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='1468', r_ui=3.0, est=3.549379811561133, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='482', r_ui=5.0, est=4.21982319020265, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='153', r_ui=3.0, est=3.7455844024243627, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='433', r_ui=3.0, est=3.4250742795412625, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='1404', r_ui=3.0, est=3.486397073488312, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='659', r_ui=5.0, est=4.426373374121641, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='1', r_ui=5.0, est=4.381324591401562, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='192', r_ui=1.0, est=3.7551192884671822, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='1039', r_ui=4.0, est=4.358550890359649, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='1025', r_ui=3.0, est=3.102867916512153, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='427', r_ui=5.0, est=4.715410010246945, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='655', r_ui=4.0, est=3.8137514264323564, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='234', r_ui=4.0, est=3.80232420502587, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='490', r_ui=5.0, est=4.3000842050636585, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='121', r_ui=5.0, est=4.033802077615374, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='699', r_ui=4.0, est=3.7066589506312733, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='82', r_ui=3.0, est=3.8051764617397357, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='132', r_ui=5.0, est=4.559480230909123, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='168', r_ui=3.0, est=3.9035108904739073, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='518', r_ui=5.0, est=4.0736428140687435, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='200', r_ui=4.0, est=3.996119041068713, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='751', r_ui=3.0, est=3.561170677773874, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='4', r_ui=4.0, est=3.561552846318996, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='966', r_ui=5.0, est=4.09966007211878, details={'was_impossible': False}),\n",
       " Prediction(uid='253', iid='318', r_ui=5.0, est=4.823641172846253, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='451', r_ui=3.0, est=2.8383142360179963, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='427', r_ui=5.0, est=4.2348776231185905, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='117', r_ui=2.0, est=2.831964676953207, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='471', r_ui=4.0, est=3.351271209523932, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='214', r_ui=2.0, est=2.429593698011302, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='425', r_ui=4.0, est=3.3674450829529246, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='71', r_ui=3.0, est=3.4084977762130744, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='654', r_ui=4.0, est=3.82730203340055, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='512', r_ui=4.0, est=3.7558962620058995, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='483', r_ui=5.0, est=4.514735551542699, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='79', r_ui=3.0, est=3.371017717046895, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='11', r_ui=1.0, est=3.0521822173864983, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='50', r_ui=5.0, est=4.050859607185961, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='189', r_ui=5.0, est=4.171858561804873, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='187', r_ui=4.0, est=4.011802040578032, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='61', r_ui=4.0, est=3.955621291352273, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='960', r_ui=1.0, est=2.941616137219797, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='923', r_ui=5.0, est=4.207086655694184, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='529', r_ui=5.0, est=4.032355587609242, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='186', r_ui=4.0, est=3.73567242492819, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='347', r_ui=3.0, est=3.467912180610319, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='203', r_ui=4.0, est=3.9052608255094503, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='15', r_ui=1.0, est=2.779126336050018, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='87', r_ui=1.0, est=2.7271342258155467, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='238', r_ui=3.0, est=3.319133646817359, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='209', r_ui=5.0, est=3.8275350398247, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='679', r_ui=3.0, est=2.919315235319069, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='56', r_ui=1.0, est=2.541290229585126, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='131', r_ui=3.0, est=3.391952706969307, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='216', r_ui=5.0, est=3.8861572976161467, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='14', r_ui=4.0, est=3.859821685011476, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='403', r_ui=2.0, est=2.7174940058461927, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='302', r_ui=4.0, est=4.012095481032488, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='210', r_ui=3.0, est=3.0363917962410247, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1411', r_ui=3.0, est=2.6378820481682514, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='169', r_ui=5.0, est=4.299211186338375, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='610', r_ui=3.0, est=3.6043405807562423, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='257', r_ui=2.0, est=2.7530158288377073, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='76', r_ui=1.0, est=2.679282955549158, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='733', r_ui=3.0, est=3.286341753552176, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='947', r_ui=4.0, est=3.3678855667114176, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1101', r_ui=4.0, est=3.7387908791339584, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='338', r_ui=3.0, est=2.651480785060512, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='212', r_ui=3.0, est=3.3507189385302847, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='298', r_ui=4.0, est=3.6840731097569113, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='192', r_ui=2.0, est=3.4320068998140787, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='151', r_ui=4.0, est=3.6605702513033047, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='806', r_ui=3.0, est=3.19588675034196, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='943', r_ui=2.0, est=2.7661575636800877, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='357', r_ui=5.0, est=4.185891664643707, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='638', r_ui=5.0, est=3.8896398962450935, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='52', r_ui=2.0, est=3.1916672187639206, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='156', r_ui=4.0, est=3.467014045525025, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='245', r_ui=1.0, est=2.068012431131822, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='249', r_ui=3.0, est=2.9702698696611867, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='660', r_ui=4.0, est=3.7838214458761974, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='602', r_ui=3.0, est=3.4096409330068775, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='154', r_ui=4.0, est=3.5901256749913193, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='239', r_ui=3.0, est=2.858772760135533, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='557', r_ui=4.0, est=3.315266014727355, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='178', r_ui=4.0, est=4.388412682375995, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='482', r_ui=2.0, est=3.295306946271278, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='188', r_ui=2.0, est=3.0755749952287132, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='511', r_ui=4.0, est=4.2020120636670795, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='204', r_ui=2.0, est=2.67824232792485, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='100', r_ui=3.0, est=3.668807389288518, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='174', r_ui=3.0, est=3.8266546955338683, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='385', r_ui=1.0, est=2.424545835494371, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='530', r_ui=5.0, est=4.005143748089675, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='190', r_ui=3.0, est=3.694876966383368, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='134', r_ui=5.0, est=4.432273133469137, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='305', r_ui=3.0, est=3.4023426903773784, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='81', r_ui=3.0, est=3.3470101806835553, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='129', r_ui=3.0, est=3.0338160839006862, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='268', r_ui=3.0, est=3.4660958076156656, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='258', r_ui=4.0, est=3.1485022201129613, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='272', r_ui=3.0, est=3.6460055409696532, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='778', r_ui=4.0, est=3.488266128601861, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1456', r_ui=4.0, est=3.5624636007371207, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='655', r_ui=4.0, est=3.5180076098724524, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='83', r_ui=3.0, est=3.8564558739430805, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='289', r_ui=4.0, est=2.845160622608008, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='207', r_ui=5.0, est=4.090523228416928, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='921', r_ui=5.0, est=4.0207728580619255, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='550', r_ui=3.0, est=2.858341895397545, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='7', r_ui=4.0, est=3.543305357991397, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='175', r_ui=4.0, est=3.427110422727891, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='405', r_ui=3.0, est=2.880710636826367, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='201', r_ui=3.0, est=3.1787519814096274, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='246', r_ui=3.0, est=3.3709519560433368, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='423', r_ui=4.0, est=3.328736576843385, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='98', r_ui=4.0, est=4.20988253804793, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='856', r_ui=5.0, est=4.005798169300249, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='527', r_ui=5.0, est=3.9742020616505624, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='237', r_ui=2.0, est=3.158541555844563, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='183', r_ui=4.0, est=4.01759280458923, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1104', r_ui=4.0, est=3.2434008329917354, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='963', r_ui=4.0, est=3.931490695177328, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='96', r_ui=3.0, est=3.296420920262624, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='628', r_ui=4.0, est=2.957894032659735, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='12', r_ui=5.0, est=3.6631657458414377, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='904', r_ui=4.0, est=3.481060827255201, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='582', r_ui=4.0, est=3.356410587684672, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='200', r_ui=3.0, est=3.0856129696320376, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='748', r_ui=3.0, est=1.9503831182203288, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='690', r_ui=4.0, est=3.3289826165046446, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='163', r_ui=3.0, est=3.524243607750093, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='88', r_ui=2.0, est=2.578168868867018, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='168', r_ui=4.0, est=3.749184886072095, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1513', r_ui=2.0, est=2.670163604185401, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='479', r_ui=3.0, est=4.009055445446489, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1015', r_ui=1.0, est=2.289477062830711, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='153', r_ui=3.0, est=3.2726971714643973, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='631', r_ui=3.0, est=3.418765913682558, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='971', r_ui=4.0, est=3.56985672017348, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='327', r_ui=3.0, est=2.953900366539274, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='64', r_ui=5.0, est=4.061361513973429, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='121', r_ui=3.0, est=2.6372215589623296, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='180', r_ui=4.0, est=3.8134108154488544, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='170', r_ui=4.0, est=4.137419735521512, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='195', r_ui=3.0, est=3.163926503831706, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='286', r_ui=4.0, est=4.062219859434379, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='792', r_ui=4.0, est=3.4069506007008235, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='16', r_ui=3.0, est=3.3285604055320452, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='223', r_ui=4.0, est=3.81411880039641, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='215', r_ui=2.0, est=2.825026401740286, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='317', r_ui=4.0, est=3.6501408101880957, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1073', r_ui=1.0, est=2.8170950449844225, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='735', r_ui=4.0, est=3.9724589968933377, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='480', r_ui=5.0, est=4.156048126345177, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='70', r_ui=4.0, est=3.4556244783240273, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='941', r_ui=2.0, est=2.5380732509780692, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='793', r_ui=5.0, est=3.8265891041291016, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='135', r_ui=3.0, est=3.2472681474969214, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='251', r_ui=5.0, est=3.992234355412903, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1512', r_ui=3.0, est=3.44909692482009, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='181', r_ui=4.0, est=3.877003875683838, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='199', r_ui=4.0, est=3.844581904218748, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='686', r_ui=3.0, est=3.274012210654947, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='184', r_ui=3.0, est=3.0484767920390365, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='202', r_ui=3.0, est=3.275511929702363, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='751', r_ui=3.0, est=3.0536468722268886, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='91', r_ui=2.0, est=3.398215349553173, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='315', r_ui=5.0, est=3.9723031675557956, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='664', r_ui=2.0, est=2.8228044688707157, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='42', r_ui=4.0, est=3.229615016474954, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='171', r_ui=5.0, est=3.773863465685131, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='179', r_ui=1.0, est=3.0374021616465816, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='770', r_ui=3.0, est=2.9760050928896993, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='282', r_ui=3.0, est=2.8764763850952817, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1485', r_ui=3.0, est=3.167909608205447, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='196', r_ui=4.0, est=3.4909598032005285, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='165', r_ui=4.0, est=4.015900275649626, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='845', r_ui=3.0, est=2.789261837405621, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='48', r_ui=5.0, est=3.890105920743964, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='143', r_ui=3.0, est=3.134954656987469, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='433', r_ui=2.0, est=3.037539498681599, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='144', r_ui=2.0, est=3.2312897343771456, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='172', r_ui=4.0, est=3.6123722877844613, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='269', r_ui=4.0, est=3.4191270001308482, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='708', r_ui=3.0, est=2.7960632377286845, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='1', r_ui=5.0, est=3.8343649850512826, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='300', r_ui=3.0, est=3.0717054399497585, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='684', r_ui=3.0, est=3.2874542262983892, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='382', r_ui=5.0, est=3.7885100097653157, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='713', r_ui=4.0, est=3.584127454062932, details={'was_impossible': False}),\n",
       " Prediction(uid='305', iid='198', r_ui=4.0, est=3.797173888470128, details={'was_impossible': False}),\n",
       " ...]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from surprise import GridSearch\n",
    "    # Select your best algo with grid search.\n",
    "print('Grid Search...')\n",
    "param_grid = {'n_epochs': [5, 10], 'lr_all': [0.002, 0.005]}\n",
    "grid_search = GridSearch(SVD, param_grid, measures=['RMSE'], verbose=1)\n",
    "print(grid_search.best_params)\n",
    "grid_search.evaluate(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating RMSE of algorithm SVD on 3 split(s).\n",
      "\n",
      "                  Fold 1  Fold 2  Fold 3  Mean    Std     \n",
      "RMSE (testset)    0.9461  0.9476  0.9432  0.9456  0.0018  \n",
      "Fit time          2.84    2.84    3.13    2.94    0.14    \n",
      "Test time         0.17    0.21    0.16    0.18    0.02    \n"
     ]
    }
   ],
   "source": [
    "algo = SVD()  # SVD(n_factors=50, random_state=0)\n",
    "results = cross_validate(algo, \n",
    "                         data,\n",
    "                         measures = ['rmse'], \n",
    "                         cv=3,\n",
    "                        verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Baseline model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating biases using als...\n",
      "RMSE: 0.9453\n",
      "Estimating biases using als...\n",
      "RMSE: 0.9377\n",
      "Estimating biases using als...\n",
      "RMSE: 0.9500\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9443304984013942"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from surprise.model_selection import KFold\n",
    "\n",
    "bsl_options = {\n",
    "    'method': 'als', #ALS - Alternating Least Squares\n",
    "    'n_epochs': 5,\n",
    "    'reg_u': 12,\n",
    "    'reg_i': 5\n",
    "}\n",
    "algo = surprise.BaselineOnly(bsl_options)\n",
    "\n",
    "np.random.seed(0)\n",
    "acc = np.zeros(3)\n",
    "cv = KFold(3)\n",
    "for i, (trainset, testset) in enumerate(cv.split(data)):\n",
    "    algo.fit(trainset)\n",
    "    predictions = algo.test(testset)\n",
    "    acc[i] = surprise.accuracy.rmse(predictions, verbose=True)\n",
    "acc.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating biases using als...\n",
      "Estimating biases using als...\n",
      "Estimating biases using als...\n",
      "Estimating biases using als...\n",
      "Estimating biases using als...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'test_rmse': array([0.9384446 , 0.94651657, 0.93612815, 0.94221861, 0.94428787]),\n",
       " 'test_mae': array([0.74477853, 0.75124267, 0.73975393, 0.745764  , 0.74659098]),\n",
       " 'fit_time': (0.07133889198303223,\n",
       "  0.07285904884338379,\n",
       "  0.0730130672454834,\n",
       "  0.07557201385498047,\n",
       "  0.07652711868286133),\n",
       " 'test_time': (0.06734895706176758,\n",
       "  0.1289689540863037,\n",
       "  0.06275510787963867,\n",
       "  0.06324410438537598,\n",
       "  0.06250905990600586)}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_validate(algo, data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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