0-Clasific-Teoria.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Presentación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://docs.google.com/presentation/d/1KrOOgNZhEeTeoh7sJ8I-Xg1459DCxXe0yuDUL43EVks/edit?usp=sharing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clasificación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\large \\underset{C_i}{arg \\ max} \\{P(C_i|X_0, X_1, ..., X_N)\\}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regresión Logística (Clasificación Binaria)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\large P(C_0|X_0, X_1, ..., X_N; W) = \\frac{1}{1+e^{-(w_0+w_1X_1+...+w_NX_N)}}$\n",
    "\n",
    "$P(C_0|X_0, X_1, ..., X_N; W) = p$\n",
    "\n",
    "$P(C_1|X_0, X_1, ..., X_N; W) = 1-p$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log odds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "\\large log\\{\\frac{p}{1-p}\\} = w_0+w_1X_1+...+w_NX_N\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regla de Bayes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "P(C_i|X_0, X_1, ..., X_N) = \\frac{P(X_0, X_1, ..., X_N|C_i)P(C_i)}{P(X_0, X_1, ..., X_N)}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log Odds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P(C_0|X_0, X_1, ..., X_N) = p$\n",
    "\n",
    "$P(C_1|X_0, X_1, ..., X_N) = 1-p$\n",
    "\n",
    "\\begin{equation}\n",
    "\\large \\frac{p}{1-p}\\ = \\frac{P(X_0, X_1, ..., X_N|C_0)P(C_0)}{P(X_0, X_1, ..., X_N|C_1)P(C_1)}\n",
    "\\end{equation}"
   ]
  }
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