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