利用TensorFlow实现多元线性回归

利用TensorFlow实现多元线性回归，代码如下：

# -*- coding:utf-8 -*-

import tensorflow as tf

import numpy as np

from sklearn import linear_model

from sklearn import preprocessing

# Read x and y

x_data = np.loadtxt("ex3x.dat").astype(np.float32)

y_data = np.loadtxt("ex3y.dat").astype(np.float32)

# We evaluate the x and y by sklearn to get a sense of the coefficients.

reg = linear_model.LinearRegression()

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.

# Before we put the x_data into tensorflow, we need to standardize it

# in order to achieve better performance in gradient descent;

# If not standardized, the convergency speed could not be tolearated.

# Reason:  If a feature has a variance that is orders of magnitude larger than others,

# it might dominate the objective function

# and make the estimator unable to learn from other features correctly as expected.

scaler = preprocessing.StandardScaler().fit(x_data)

print (scaler.mean_, scaler.scale_)

x_data_standard = scaler.transform(x_data)

W = tf.Variable(tf.zeros([2, 1]))

b = tf.Variable(tf.zeros([1, 1]))

y = tf.matmul(x_data_standard, W) + b

loss = tf.reduce_mean(tf.square(y - y_data.reshape(-1, 1)))/2

optimizer = tf.train.GradientDescentOptimizer(0.3)

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))))

数据集下载：下载地址