利用TensorFlow实现多元逻辑回归
2017-05-12 11:22 猎手家园 阅读(2197) 评论(0) 编辑 收藏 举报利用TensorFlow实现多元逻辑回归,代码如下:
import tensorflow as tf import numpy as np from sklearn.linear_model import LogisticRegression from sklearn import preprocessing # Read x and y x_data = np.loadtxt("ex4x.dat").astype(np.float32) y_data = np.loadtxt("ex4y.dat").astype(np.float32) scaler = preprocessing.StandardScaler().fit(x_data) x_data_standard = scaler.transform(x_data) # We evaluate the x and y by sklearn to get a sense of the coefficients. reg = LogisticRegression(C=999999999, solver="newton-cg") # Set C as a large positive number to minimize the regularization effect reg.fit(x_data, y_data) print ("Coefficients of sklearn: K=%s, b=%f" % (reg.coef_, reg.intercept_)) # Now we use tensorflow to get similar results. W = tf.Variable(tf.zeros([2, 1])) b = tf.Variable(tf.zeros([1, 1])) y = 1 / (1 + tf.exp(-tf.matmul(x_data_standard, W) + b)) loss = tf.reduce_mean(- y_data.reshape(-1, 1) * tf.log(y) - (1 - y_data.reshape(-1, 1)) * tf.log(1 - y)) optimizer = tf.train.GradientDescentOptimizer(1.3) train = optimizer.minimize(loss) init = tf.initialize_all_variables() sess = tf.Session() sess.run(init) for step in range(100): sess.run(train) if step % 10 == 0: print (step, sess.run(W).flatten(), sess.run(b).flatten()) print ("Coefficients of tensorflow (input should be standardized): K=%s, b=%s" % (sess.run(W).flatten(), sess.run(b).flatten())) print ("Coefficients of tensorflow (raw input): K=%s, b=%s" % (sess.run(W).flatten() / scaler.scale_, sess.run(b).flatten() - np.dot(scaler.mean_ / scaler.scale_, sess.run(W)))) # Problem solved and we are happy. But... # I'd like to implement the logistic regression from a multi-class viewpoint instead of binary. # In machine learning domain, it is called softmax regression # In economic and statistics domain, it is called multinomial logit (MNL) model, proposed by Daniel McFadden, who shared the 2000 Nobel Memorial Prize in Economic Sciences. print ("------------------------------------------------") print ("We solve this binary classification problem again from the viewpoint of multinomial classification") print ("------------------------------------------------") # As a tradition, sklearn first reg = LogisticRegression(C=9999999999, solver="newton-cg", multi_class="multinomial") reg.fit(x_data, y_data) print ("Coefficients of sklearn: K=%s, b=%f" % (reg.coef_, reg.intercept_)) print ("A little bit difference at first glance. What about multiply them with 2?") # Then try tensorflow W = tf.Variable(tf.zeros([2, 2])) # first 2 is feature number, second 2 is class number b = tf.Variable(tf.zeros([1, 2])) V = tf.matmul(x_data_standard, W) + b y = tf.nn.softmax(V) # tensorflow provide a utility function to calculate the probability of observer n choose alternative i, you can replace it with `y = tf.exp(V) / tf.reduce_sum(tf.exp(V), keep_dims=True, reduction_indices=[1])` # Encode the y label in one-hot manner lb = preprocessing.LabelBinarizer() lb.fit(y_data) y_data_trans = lb.transform(y_data) y_data_trans = np.concatenate((1 - y_data_trans, y_data_trans), axis=1) # Only necessary for binary class loss = tf.reduce_mean(-tf.reduce_sum(y_data_trans * tf.log(y), reduction_indices=[1])) optimizer = tf.train.GradientDescentOptimizer(1.3) train = optimizer.minimize(loss) init = tf.initialize_all_variables() sess = tf.Session() sess.run(init) for step in range(100): sess.run(train) if step % 10 == 0: print (step, sess.run(W).flatten(), sess.run(b).flatten()) print ("Coefficients of tensorflow (input should be standardized): K=%s, b=%s" % (sess.run(W).flatten(), sess.run(b).flatten())) print ("Coefficients of tensorflow (raw input): K=%s, b=%s" % ((sess.run(W) / scaler.scale_).flatten(), sess.run(b).flatten() - np.dot(scaler.mean_ / scaler.scale_, sess.run(W))))
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