Learning from Data: Logistic Regression Exercise

logistic.py

import numpy as np

# Find f(x), where f is the line through p1 and p2
def f(p1, p2, x):
    return (p2[1]-p1[1])/(p2[0]-p1[0])*(x-p1[0])+p1[1]
  
epochs = []
Eouts = []

N = 100
for i in range(N):
    # Initialize function
    # Get random points p1 and p2
    p1, p2 = 2*np.random.rand(2, 2)-1
    line = lambda x: f(p1, p2, x)
    def label(p):
        return np.sign(p[1]-line(p[0]))
    
    # Initialize model training
    w = np.zeros((3), dtype=np.float)
    epoch = 0
    delta = 1
    eta = 0.01    
    training_set = np.concatenate((2*np.random.rand(100, 2)-1,
                                   np.ones((100, 1), dtype=np.float)),
                                  axis=1)
    # Train model
    while delta >= 0.01:
        epoch += 1
        last_w = np.copy(w)
        np.random.shuffle(training_set)
        for p in training_set:
            w += eta*np.divide(label(p)*p, 
                               1+np.exp(label(p)*np.dot(w,p)))
        delta = np.linalg.norm(last_w-w)
    epochs.append(epoch)
    
    # Test model
    test_set = np.concatenate((2*np.random.rand(100, 2)-1,
                               np.ones((100, 1), dtype=np.float)),
                              axis=1)
    error = 1/N*sum([np.log(1+np.exp(-label(p)*np.dot(w,p))) for p in test_set])
    Eouts.append(error)