ml-class - ex1 (python)

ex1.py

#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
from numpy import newaxis, r_, c_, mat
from numpy.linalg import *

def plotData(X, y):
    plt.plot(X, y, 'rx', markersize=7)
    plt.ylabel('Profit in $10,000s')
    plt.xlabel('Population of City in 10,000s')

def computeCost(X, y, theta):
    m = X.shape[0]

    predictions = X*theta
    sqrErrors = (predictions - y).A ** 2
    return 1./(2*m) * sqrErrors.sum()

def gradientDescent(X, y, theta, alpha, num_iters):
    m = X.shape[0]

    J_history = np.zeros(num_iters)
    for i in xrange(num_iters):
        theta = theta - alpha/m * X.T * (X*theta - y)
        J_history[i] = computeCost(X, y, theta)
    return theta, J_history

if __name__ == '__main__':
    data = np.loadtxt('ex1data1.txt', delimiter=',')
    X = mat(data[:, 0][:, newaxis])
    y = data[:, 1][:, newaxis]
    m = X.shape[0]

    # =================== Part 2: Plotting

    plotData(X, y)
    plt.show()

    raw_input('Press any key to continue\n')

    # =================== Part 3: Gradient descent

    X = c_[np.ones(m), X]
    theta = np.zeros(2)[:, newaxis]

    iterations = 1500
    alpha = 0.01

    print computeCost(X, y, theta)

    theta, J_history = gradientDescent(X, y, theta, alpha, iterations)

    print 'Theta found by gradient descent:\n', theta
    plotData(X[:, 1], y)
    plt.plot(X[:, 1], X*theta, '-')
    plt.legend(['Training data', 'Linear regression'])
    plt.show()

    raw_input('Press any key to continue\n')

    # ============= Part 4: Visualizing J(theta_0, theta_1)

    theta0_vals = np.linspace(-10, 10, 100)
    theta1_vals = np.linspace(-1, 4, 100)

    J_vals = np.zeros((len(theta0_vals), len(theta1_vals)))

    for i in xrange(len(theta0_vals)):
        for j in xrange(len(theta1_vals)):
            t = r_[theta0_vals[i], theta1_vals[j]][:, newaxis]
            J_vals[i, j] = computeCost(X, y, t);

    J_vals = J_vals.T
    plt.contour(theta0_vals, theta1_vals, J_vals, np.logspace(-2, 3, 20))
    plt.plot(theta[0], theta[1], 'rx', markersize=10, linewidth=5)
    plt.xlabel(r'$\Theta_0$'); plt.ylabel(r'$\Theta_1$')
    plt.show()