tensorflow 梯度下降

tensorflow 梯度下降

import tensorflow as tfimport numpy as npimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import Axes3D# LR = 0.1LR = .1REAL_PARAMS = [1.2, 2.5]INIT_PARAMS = [[5, 4], [5, 1], [2, 4.5]][2]x = np.linspace(-1, 1, 200, dtype=np.float32) # x data# Test (1): Visualize a simple linear function with two parameters,# you can change LR to 1 to see the different pattern in gradient descent.# y_fun = lambda a, b: a * x + b# tf_y_fun = lambda a, b: a * x + b# Test (2): Using Tensorflow as a calibrating tool for empirical formula like following.y_fun = lambda a, b: a * x**3 + b * x**2tf_y_fun = lambda a, b: a * x**3 + b * x**2# Test (3): Most simplest two parameters and two layers Neural Net, and their local & global minimum,# you can try different INIT_PARAMS set to visualize the gradient descent.# y_fun = lambda a, b: np.sin(b*np.cos(a*x))# tf_y_fun = lambda a, b: tf.sin(b*tf.cos(a*x))noise = np.random.randn(200)/10y = y_fun(*REAL_PARAMS) + noise # target# tensorflow grapha, b = [tf.Variable(initial_value=p, dtype=tf.float32) for p in INIT_PARAMS]pred = tf_y_fun(a, b)mse = tf.reduce_mean(tf.square(y-pred))train_op = tf.train.GradientDescentOptimizer(LR).minimize(mse)a_list, b_list, cost_list = [], [], []with tf.Session() as sess: sess.run(tf.global_variables_initializer()) for t in range(400): a_, b_, mse_ = sess.run([a, b, mse]) a_list.append(a_); b_list.append(b_); cost_list.append(mse_) # record parameter changes result, _ = sess.run([pred, train_op]) # training# visualization codes:print('a=', a_, 'b=', b_)plt.figure(1)plt.scatter(x, y, c='b') # plot dataplt.plot(x, result, 'r-', lw=2) # plot line fitting# 3D cost figurefig = plt.figure(2); ax = Axes3D(fig)a3D, b3D = np.meshgrid(np.linspace(-2, 7, 30), np.linspace(-2, 7, 30)) # parameter spacecost3D = np.array([np.mean(np.square(y_fun(a_, b_) - y)) for a_, b_ in zip(a3D.flatten(), b3D.flatten())]).reshape(a3D.shape)ax.plot_surface(a3D, b3D, cost3D, rstride=1, cstride=1, cmap=plt.get_cmap('rainbow'), alpha=0.5)ax.scatter(a_list[0], b_list[0], zs=cost_list[0], s=300, c='r') # initial parameter placeax.set_xlabel('a'); ax.set_ylabel('b')ax.plot(a_list, b_list, zs=cost_list, zdir='z', c='r', lw=3) # plot 3D gradient descentplt.show()

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