gradient descent algorithm

grad.py

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

def hypothesis(x, theta):
    """function"""
    return x.dot(theta).sum()

def compute_cost(X, Y, theta):
    """errors"""
    m = Y.size
    predictions = X.dot(theta).flatten()
    errors = (Y - predictions)**2
    result = 1
    J  = (1./ 2/ m) * errors.sum()
    return J

def descent(X, Y, theta, alpha=0.001, iter_count=1000):
    m = Y.size
    new_theta = [0]*len(theta)
    for i in range(iter_count):
        predictions = X.dot(theta).flatten()
        for j in range(len(theta)):
            errors = (predictions - Y) * X[:, j]
            new_theta[j] = theta[j] - alpha * (1./m) * errors.sum()
        theta = new_theta
    return theta


"""
   h(x) = t0x0 + t1x1 + t2x2 + t3x3
"""

x = np.random.rand(2,2)
x_cap = map(np.linalg.norm , x)
theta = np.array([[1],[1]])
y = np.random.rand(2, 1)
h = hypothesis
print(theta)
theta = descent(x, y, theta, iter_count=100000, alpha=0.25)
print(theta)
y_cap = map(lambda l: hypothesis(l, theta), x)
beta_hat = np.linalg.lstsq(x,y)
print(beta_hat)
plt.plot(x_cap, y, 'r-' ,label="data plot")
plt.plot(x_cap, beta_hat[0], 'g-', label="hypothesis methodof least squares plot")
plt.plot(x_cap, y_cap, 'b-', label="descent")
plt.xlabel("X - axis")
plt.ylabel("Y - axis")
plt.show()