3.TensorFlow非线性回归例子

 下面是一个非线性回归的例子，代码如下：

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt

#使用numpy生成200个随机点
x_data = np.linspace(-0.5,0.5,200)[:,np.newaxis]
noise = np.random.normal(0,0.02,x_data.shape)
y_data = np.square(x_data) + noise

#定义两个placeholder
x = tf.placeholder(tf.float32,[None,1])
y = tf.placeholder(tf.float32,[None,1])

#定义神经网络中间层
Weights_L1 = tf.Variable(tf.random_normal([1,10]))
biases_L1 = tf.Variable(tf.zeros([1,10]))
Wx_plus_b_L1 = tf.matmul(x,Weights_L1) + biases_L1
L1 = tf.nn.tanh(Wx_plus_b_L1)

#定义神经网络输出层
Weights_L2 = tf.Variable(tf.random_normal([10,1]))
biases_L2 = tf.Variable(tf.zeros([1,1]))
Wx_plus_b_L2 = tf.matmul(L1,Weights_L2) + biases_L2
prediction = tf.nn.tanh(Wx_plus_b_L2)

#二次代价函数
loss = tf.reduce_mean(tf.square(y-prediction))
#使用梯度下降法训练
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

with tf.Session() as sess:
    #变量初始化
    sess.run(tf.global_variables_initializer())
    for _ in range(2000):
        sess.run(train_step,feed_dict={x:x_data,y:y_data})
        
    #获得预测值
    prediction_value = sess.run(prediction,feed_dict={x:x_data})
    #画图
    plt.figure()
    plt.scatter(x_data,y_data)
    plt.plot(x_data,prediction_value,'r-',lw=5)
    plt.show()

在上面的例子中，我们想要预测的方程式y=x*x,给定训练样本，通过梯度下降法来预测参数W和偏置b，我们使用numpy生成了我们的训练数据：

代码讲解：

1.加入相应的库

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt

2，定义变量

x_data = np.linspace(-0.5,0.5,200)[:,np.newaxis]
noise = np.random.normal(0,0.02,x_data.shape)
y_data = np.square(x_data) + noise

3定义网络结构 及其代价函数 优化器

#定义神经网络中间层
Weights_L1 = tf.Variable(tf.random_normal([1,10]))
biases_L1 = tf.Variable(tf.zeros([1,10]))
Wx_plus_b_L1 = tf.matmul(x,Weights_L1) + biases_L1
L1 = tf.nn.tanh(Wx_plus_b_L1)

#定义神经网络输出层
Weights_L2 = tf.Variable(tf.random_normal([10,1]))
biases_L2 = tf.Variable(tf.zeros([1,1]))
Wx_plus_b_L2 = tf.matmul(L1,Weights_L2) + biases_L2
prediction = tf.nn.tanh(Wx_plus_b_L2)

#二次代价函数
loss = tf.reduce_mean(tf.square(y-prediction))
#使用梯度下降法训练
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

4，启动计算图

with tf.Session() as sess:
    #变量初始化
    sess.run(tf.global_variables_initializer())
    for _ in range(2000):
        sess.run(train_step,feed_dict={x:x_data,y:y_data})
        
    #获得预测值
    prediction_value = sess.run(prediction,feed_dict={x:x_data})
    #画图
    plt.figure()
    plt.scatter(x_data,y_data)
    plt.plot(x_data,prediction_value,'r-',lw=5)
    plt.show()