TensorFlow(三)：非線性迴歸

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

# 非線性迴歸

# 使用numpy生成200個隨機點

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

# 定義兩個placeholder
x=tf.placeholder(tf.float32,[None,1])
y=tf.placeholder(tf.float32,[None,1])

# 定義神經網絡的中間層
Weights_L1=tf.Variable(tf.random_normal([1,10])) # 權重，輸入層爲1，中間層爲10個
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) # 使用雙曲正切做爲激活函數

# 定義輸出層
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)

# 二次代價函數
loss=tf.reduce_mean(tf.square(y-prediction))
# 使用梯度降低法
train_step=tf.train.GradientDescentOptimizer(0.1).minimize(loss)# 最小化loss

with tf.Session() as sess:
    # 變量初始化
    sess.run(tf.global_variables_initializer())
    for _ in range(2000):
        sess.run(train_step,feed_dict={x:x_data,y:y_data}) # 傳入參數
        
    # 得到預測值
    prediction_value=sess.run(prediction,feed_dict={x:x_data})
    
    # 畫圖
    plt.figure()
    plt.scatter(x_data,y_data)
    plt.plot(x_data,prediction_value,'r-',lw=5)
    plt.show()