我们用Tensorflow实现线性回归（linear regression learning）算法：

首先，导入需要的包：

import tensorflow as tf
import numpy
import matplotlib.pyplot as plt
rng = numpy.random

设置训练的参数：

# Parameters
learning_rate = 0.01
training_epochs = 1000
display_step = 50

其中，learning_rate是梯度下降的速率，training_epochs是训练时的最大迭代次数，display_step用于将训练的信息打印出来，打印前50步的信息。

然后是读取训练集数据

# Training Data
train_X = numpy.asarray([3.3,4.4,5.5,6.71,6.93,4.168,9.779,6.182,7.59,2.167,
                         7.042,10.791,5.313,7.997,5.654,9.27,3.1])
train_Y = numpy.asarray([1.7,2.76,2.09,3.19,1.694,1.573,3.366,2.596,2.53,1.221,
                         2.827,3.465,1.65,2.904,2.42,2.94,1.3])
n_samples = train_X.shape[0]

# tf Graph Input
X = tf.placeholder("float")
Y = tf.placeholder("float")

# Set model weights
W = tf.Variable(rng.randn(), name="weight")
b = tf.Variable(rng.randn(), name="bias")

构建线性模型：

# Construct a linear model
pred = tf.add(tf.multiply(X, W), b)

以Mean squared error作为训练的目标函数：

# Mean squared error
cost = tf.reduce_sum(tf.pow(pred-Y, 2))/(2*n_samples)
# Gradient descent
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

初始化变量

# Initialize the variables (i.e. assign their default value)
init = tf.global_variables_initializer()

开始训练：

# Start training
with tf.Session() as sess:
    sess.run(init)

    # Fit all training data
    for epoch in range(training_epochs):
        for (x, y) in zip(train_X, train_Y):
            sess.run(optimizer, feed_dict={X: x, Y: y})

        #Display logs per epoch step
        if (epoch+1) % display_step == 0:
            c = sess.run(cost, feed_dict={X: train_X, Y:train_Y})
            print "Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(c), \
                "W=", sess.run(W), "b=", sess.run(b)

    print "Optimization Finished!"
    training_cost = sess.run(cost, feed_dict={X: train_X, Y: train_Y})
    print "Training cost=", training_cost, "W=", sess.run(W), "b=", sess.run(b), '\n'

    #Graphic display
    plt.plot(train_X, train_Y, 'ro', label='Original data')
    plt.plot(train_X, sess.run(W) * train_X + sess.run(b), label='Fitted line')
    plt.legend()
    plt.show()

程序的输出：

Epoch: 0050 cost= 0.195095107 W= 0.441748 b= -0.580876
Epoch: 0100 cost= 0.181448311 W= 0.430319 b= -0.498661
Epoch: 0150 cost= 0.169377610 W= 0.419571 b= -0.421336
Epoch: 0200 cost= 0.158700854 W= 0.409461 b= -0.348611
Epoch: 0250 cost= 0.149257123 W= 0.399953 b= -0.28021
Epoch: 0300 cost= 0.140904188 W= 0.391011 b= -0.215878
Epoch: 0350 cost= 0.133515999 W= 0.3826 b= -0.155372
Epoch: 0400 cost= 0.126981199 W= 0.374689 b= -0.0984639
Epoch: 0450 cost= 0.121201262 W= 0.367249 b= -0.0449408
Epoch: 0500 cost= 0.116088994 W= 0.360252 b= 0.00539905
Epoch: 0550 cost= 0.111567356 W= 0.35367 b= 0.052745
Epoch: 0600 cost= 0.107568085 W= 0.34748 b= 0.0972751
Epoch: 0650 cost= 0.104030922 W= 0.341659 b= 0.139157
Epoch: 0700 cost= 0.100902475 W= 0.336183 b= 0.178547
Epoch: 0750 cost= 0.098135538 W= 0.331033 b= 0.215595
Epoch: 0800 cost= 0.095688373 W= 0.32619 b= 0.25044
Epoch: 0850 cost= 0.093524046 W= 0.321634 b= 0.283212
Epoch: 0900 cost= 0.091609895 W= 0.317349 b= 0.314035
Epoch: 0950 cost= 0.089917004 W= 0.31332 b= 0.343025
Epoch: 1000 cost= 0.088419855 W= 0.30953 b= 0.370291
Optimization Finished!
Training cost= 0.0884199 W= 0.30953 b= 0.370291 

最终训练结果：

image.png