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Move Gradient Descent comparison notebook to 'extra_...' and remove .py version

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Aurélien Geron 2018-09-17 11:43:34 +02:00
parent c13d4c322b
commit de6678beb1
2 changed files with 0 additions and 129 deletions
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gradient_descent_comparison.ipynb → extra_gradient_descent_comparison.ipynb
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gradient_descent_comparison.py
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from __future__ import print_function, division, unicode_literals
import sys
from math import sqrt
import numpy as np
import matplotlib.pyplot as plt
m = 100
X = 2*np.random.rand(m, 1)
X_b = np.c_[np.ones((m, 1)), X]
y = 4 + 3*X + np.random.rand(m, 1)
fig = plt.figure(figsize=(10, 5))
data_ax = fig.add_subplot(121)
cost_ax = fig.add_subplot(122)
def batch_gradient_descent():
n_iterations = 1000
learning_rate = 0.05
thetas = np.random.randn(2, 1)
thetas_path = [thetas]
for i in range(n_iterations):
gradients = 2*X_b.T.dot(X_b.dot(thetas) - y)/m
thetas = thetas - learning_rate*gradients
thetas_path.append(thetas)
return thetas_path
def stochastic_gradient_descent():
n_epochs = 50
t0, t1 = 5, 50
thetas = np.random.randn(2, 1)
thetas_path = [thetas]
for epoch in range(n_epochs):
for i in range(m):
random_index = np.random.randint(m)
xi = X_b[random_index:random_index+1]
yi = y[random_index:random_index+1]
gradients = 2*xi.T.dot(xi.dot(thetas) - yi)
eta = learning_schedule(epoch*m + i, t0, t1)
thetas = thetas - eta*gradients
thetas_path.append(thetas)
return thetas_path
def mini_batch_gradient_descent():
n_iterations = 50
minibatch_size = 20
t0, t1 = 200, 1000
thetas = np.random.randn(2, 1)
thetas_path = [thetas]
t = 0
for epoch in range(n_iterations):
shuffled_indices = np.random.permutation(m)
X_b_shuffled = X_b[shuffled_indices]
y_shuffled = y[shuffled_indices]
for i in range(0, m, minibatch_size):
t += 1
xi = X_b_shuffled[i:i+minibatch_size]
yi = y_shuffled[i:i+minibatch_size]
gradients = 2*xi.T.dot(xi.dot(thetas) - yi)/minibatch_size
eta = learning_schedule(t, t0, t1)
thetas = thetas - eta*gradients
thetas_path.append(thetas)
return thetas_path
def compute_mse(theta):
return np.sum((np.dot(X_b, theta) - y)**2)/m
def learning_schedule(t, t0, t1):
return t0/(t+t1)
if __name__ == '__main__':
plt.ion()
theta0, theta1 = np.meshgrid(np.arange(0, 5, 0.1), np.arange(0, 5, 0.1))
r, c = theta0.shape
cost_map = np.array([[0 for _ in range(c)] for _ in range(r)])
for i in range(r):
for j in range(c):
theta = np.array([theta0[i,j], theta1[i,j]])
cost_map[i,j] = compute_mse(theta)
exact_solution = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)
bgd_thetas = np.array(batch_gradient_descent())
sgd_thetas = np.array(stochastic_gradient_descent())
mbgd_thetas = np.array(mini_batch_gradient_descent())
bgd_len = len(bgd_thetas)
sgd_len = len(sgd_thetas)
mbgd_len = len(mbgd_thetas)
n_iter = min(bgd_len, sgd_len, mbgd_len)
cost_ax.plot(exact_solution[0,0], exact_solution[1,0], 'y*')
cost_img = cost_ax.pcolor(theta0, theta1, cost_map)
fig.colorbar(cost_img)
for i in range(n_iter):
data_ax.cla()
cost_ax.cla()
data_ax.plot(X, y, 'k.')
cost_ax.plot(exact_solution[0,0], exact_solution[1,0], 'y*')
cost_ax.pcolor(theta0, theta1, cost_map)
data_ax.plot(X, X_b.dot(bgd_thetas[i,:]), 'r-')
cost_ax.plot(bgd_thetas[:i,0], bgd_thetas[:i,1], 'r--')
data_ax.plot(X, X_b.dot(sgd_thetas[i,:]), 'g-')
cost_ax.plot(sgd_thetas[:i,0], sgd_thetas[:i,1], 'g--')
data_ax.plot(X, X_b.dot(mbgd_thetas[i,:]), 'b-')
cost_ax.plot(mbgd_thetas[:i,0], mbgd_thetas[:i,1], 'b--')
data_ax.set_xlim([0, 2])
data_ax.set_ylim([0, 15])
cost_ax.set_xlim([0, 5])
cost_ax.set_ylim([0, 5])
data_ax.set_xlabel(r'$x_1$')
data_ax.set_ylabel(r'$y$')
cost_ax.set_xlabel(r'$\theta_0$')
cost_ax.set_ylabel(r'$\theta_1$')
data_ax.legend(('Data', 'BGD', 'SGD', 'MBGD'))
cost_ax.legend(('Normal Equation', 'BGD', 'SGD', 'MBGD'))
plt.pause(1e-5)