02 线性回归与非线性回归

线性回归

import tensorflow as tf
import numpy as np

# 生成100个随机点
x_data = np.random.rand(100)
y_data = x_data * 0.1 + 0.2

# 创建一个线性模型
b = tf.Variable(0.)
k = tf.Variable(0.)
y = k * x_data + b

# 二次代价函数
loss = tf.reduce_mean(tf.square(y_data - y))

#创建一个梯度下降优化器
optimizer = tf.train.GradientDescentOptimizer(0.2)

# 最小化代价函数 
train = optimizer.minimize(loss)

# 变量初始化
init =  tf.global_variables_initializer()

with tf.Session() as sess:
    sess.run(init)
    # 迭代200轮
    for step in range(201):
        sess.run(train)
        # 每20次打印一次计算结果
        if step % 20 == 0:
            print(step,sess.run([k,b]))

执行结果：

0 [0.057367086, 0.10127523]
20 [0.10597865, 0.19659111]
40 [0.10346817, 0.19802256]
60 [0.10201186, 0.1988529]
80 [0.10116707, 0.19933458]
100 [0.10067701, 0.19961399]
120 [0.10039274, 0.19977607]
140 [0.10022783, 0.19987011]
160 [0.10013214, 0.19992466]
180 [0.10007665, 0.1999563]
200 [0.10004447, 0.19997464]

非线性回归

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

# 使用numpy 生成200个随机点，范围在-0.5--0.5之间，产生了200行1列的矩阵
# newaxis = None
x_data = np.linspace(-0.5,0.5,200)[:,np.newaxis]

# 产生随机噪声
noise = np.random.normal(0,0.02,x_data.shape)

# 给y_data 加入噪声
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])

# 定义神经网络的中间层，中间层的权值为1行10列的矩阵
Weights_L1 = tf.Variable(tf.random_normal([1,10]))
# 产生偏置值
biases_L1 = tf.Variable(tf.zeros([1,10]))
# 预测结果：y = x * w + b
Wx_plus_b_L1 = tf.matmul(x,Weights_L1) + biases_L1

# 激活函数使用tanh
L1 = tf.nn.tanh(Wx_plus_b_L1)

# 定义输出层，权重为10行1列
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))
# 使用梯度下降法进行训练
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    for _ in range(2000):
        sess.run(train_step,feed_dict={x:x_data,y:y_data})

    # 获取预测值
    prediction_value = sess.run(prediction,feed_dict={x:x_data})

    # 画图
    plt.figure()
    #绘制散点图
    plt.scatter(x_data,y_data)
    plt.plot(x_data,prediction_value,'r-',lw=5)
    plt.show()

执行结果：