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gradient_descent
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import numpy as np | |
import random | |
def gradient_descent(alpha, x, y, ep=0.0001, max_iter=10000): | |
converged = False | |
iter = 0 | |
m = x.shape[0] # number of samples | |
# initial theta | |
t0 = np.random.random(x.shape[1]) | |
t1 = np.random.random(x.shape[1]) | |
# total error, J(theta) | |
J = sum([(t0 + t1*x[i] - y[i])**2 for i in range(m)]) | |
# Iterate Loop | |
while not converged: | |
# for each training sample, compute the gradient (d/d_theta j(theta)) | |
grad0 = 1.0/m * sum([(t0 + t1*x[i] - y[i]) for i in range(m)]) | |
grad1 = 1.0/m * sum([(t0 + t1*x[i] - y[i])*x[i] for i in range(m)]) | |
# update the theta_temp | |
temp0 = t0 - alpha * grad0 | |
temp1 = t1 - alpha * grad1 | |
# update theta | |
t0 = temp0 | |
t1 = temp1 | |
# mean squared error | |
e = sum( [ (t0 + t1*x[i] - y[i])**2 for i in range(m)] ) | |
if abs(J-e) <= ep: | |
print 'Converged, iterations: ', iter, '!!!' | |
converged = True | |
J = e # update error | |
iter += 1 # update iter | |
if iter == max_iter: | |
print 'Max interactions exceeded!' | |
converged = True | |
return t0,t1 |
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