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131 lines
4.0 KiB
131 lines
4.0 KiB
import numpy as np
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import matplotlib.pyplot as plt
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###############################
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#Datos originales
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###############################
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X = 2 * np.random.rand(100, 1)
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y = 4 + 3 * X + np.random.randn(100,1)
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###############################
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eta = 0.1
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n_iterations = 1000
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m = 100
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X_b = np.c_[np.ones((100, 1)), X] # add x0 = 1 to each instance
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theta = np.random.randn(2,1)
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X_new = np.array([[0], [2]])
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X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance
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for iteration in range(n_iterations):
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gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)
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theta = theta - eta * gradients
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theta_path_bgd = []
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def plot_gradient_descent(theta, eta, theta_path=None):
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m = len(X_b)
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plt.plot(X, y, "b.")
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n_iterations = 1000
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for iteration in range(n_iterations):
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if iteration < 10:
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y_predict = X_new_b.dot(theta)
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style = "b-" if iteration > 0 else "r--"
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plt.plot(X_new, y_predict, style)
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gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)
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theta = theta - eta * gradients
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if theta_path is not None:
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theta_path.append(theta)
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plt.xlabel("$x_1$", fontsize=18)
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plt.axis([0, 2, 0, 15])
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plt.title(r"$\eta = {}$".format(eta), fontsize=16)
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np.random.seed(42)
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theta = np.random.randn(2,1) # random initialization
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plt.figure(figsize=(10,4))
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plt.subplot(131); plot_gradient_descent(theta, eta=0.02)
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plt.ylabel("$y$", rotation=0, fontsize=18)
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plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)
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plt.subplot(133); plot_gradient_descent(theta, eta=0.5)
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plt.show()
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theta_path_sgd = []
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m = len(X_b)
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np.random.seed(42)
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n_epochs = 50
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t0, t1 = 5, 50 # learning schedule hyperparameters
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def learning_schedule(t):
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return t0 / (t + t1)
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theta = np.random.randn(2,1) # random initialization
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for epoch in range(n_epochs):
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for i in range(m):
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if epoch == 0 and i < 20: # not shown in the book
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y_predict = X_new_b.dot(theta) # not shown
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style = "b-" if i > 0 else "r--" # not shown
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plt.plot(X_new, y_predict, style) # not shown
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random_index = np.random.randint(m)
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xi = X_b[random_index:random_index+1]
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yi = y[random_index:random_index+1]
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gradients = 2 * xi.T.dot(xi.dot(theta) - yi)
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eta = learning_schedule(epoch * m + i)
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theta = theta - eta * gradients
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theta_path_sgd.append(theta) # not shown
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plt.plot(X, y, "b.") # not shown
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plt.xlabel("$x_1$", fontsize=18) # not shown
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plt.ylabel("$y$", rotation=0, fontsize=18) # not shown
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plt.axis([0, 2, 0, 15]) # not shown
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plt.show() # not shown
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theta_path_mgd = []
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n_iterations = 50
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minibatch_size = 20
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np.random.seed(42)
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theta = np.random.randn(2,1) # random initialization
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t0, t1 = 200, 1000
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def learning_schedule(t):
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return t0 / (t + t1)
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t = 0
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for epoch in range(n_iterations):
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shuffled_indices = np.random.permutation(m)
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X_b_shuffled = X_b[shuffled_indices]
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y_shuffled = y[shuffled_indices]
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for i in range(0, m, minibatch_size):
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t += 1
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xi = X_b_shuffled[i:i+minibatch_size]
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yi = y_shuffled[i:i+minibatch_size]
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gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)
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eta = learning_schedule(t)
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theta = theta - eta * gradients
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theta_path_mgd.append(theta)
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theta_path_bgd = np.array(theta_path_bgd)
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theta_path_sgd = np.array(theta_path_sgd)
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theta_path_mgd = np.array(theta_path_mgd)
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plt.figure(figsize=(7,4))
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plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], "r-s", linewidth=1, label="Stochastic")
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plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], "g-+", linewidth=2, label="Mini-batch")
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plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], "b-o", linewidth=3, label="Batch")
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plt.legend(loc="upper left", fontsize=16)
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plt.xlabel(r"$\theta_0$", fontsize=20)
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plt.ylabel(r"$\theta_1$ ", fontsize=20, rotation=0)
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plt.axis([2.5, 4.5, 2.3, 3.9])
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plt.show()
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