first commit

hw1 (ERM, true risk)/hw1.py

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+#!/usr/bin/env python
+import random
+
+import numpy as np
+from matplotlib import pyplot
+
+
+def generate_sample(m, rect_size):
+    return [(random.uniform(0, rect_size), random.uniform(0, rect_size)) for _ in range(m)]
+
+
+def true_risk(sample, rectX_size, rectQ_size):
+    q_points = [point for point in sample if point[0] <= rectQ_size and point[1] <= rectQ_size]
+    rect_area = 0
+    if len(q_points) > 1:
+        x = list(map(lambda point: point[0], q_points))
+        y = list(map(lambda point: point[1], q_points))
+        rect_area = (max(x) - min(x)) * (max(y) - min(y))
+    return (rectQ_size ** 2 - rect_area) / rectX_size ** 2
+
+
+def single_experiment(m, rectX_size, rectQ_size):
+    sample = generate_sample(m, rectX_size)
+    return true_risk(sample, rectX_size, rectQ_size)
+
+
+rectX_size = 1.0
+rectQ_size = 0.5 ** 0.5
+
+x = range(1, 500)
+y = [single_experiment(m, rectX_size, rectQ_size) for m in x]
+pyplot.plot(x, y)
+pyplot.show()
+
+
+def calculate_min_m(m_start, e):
+    m = m_start
+    true_risk = 1
+    while true_risk > e:
+        trials = [single_experiment(m, rectX_size, rectQ_size) for _ in range(10)]
+        true_risk = np.mean(trials)
+        m += 1
+    return m
+
+
+e = [0.1, 0.01, 0.001]
+m = [None] * len(e)
+for i in range(len(e)):
+    m_start = 1 if i == 0 else m[i - 1]
+    m[i] = calculate_min_m(m_start, e[i])
+
+for m_i, e_i in zip(m, e):
+    print('m = {} for true_risk = {}'.format(m_i, e_i))