TensorFlow实战--单变量线性回归

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北山啦 发表于 2021/04/10 22:50:09 2021/04/10
【摘要】 TensorFlow实战--单变量线性回归

TensorFlow实战--单变量线性回归

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使用tensorflow实现单变量回归模型

@[toc] 使用TensorFlow进行算法设计与训练的核心步骤

  1. 准备数据

  2. 构建模型

  3. 训练模型

  4. 进行预测

上述步骤是我们使用TensorFlow进行算法设计与训练的核心步骤，贯穿于具体实践中。

监督式机器学习的基本术语

标签和特征

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训练

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损失

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定义损失函数

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模型训练与降低损失

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样本和模型

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线性回归问题TensorFlow实战

人工数据生成

 import warnings
 warnings.filterwarnings("ignore")
 import tensorflow as tf
 import numpy as np
 import matplotlib.pyplot as plt
 np.random.seed(5)

使用numpy生成等差数列的方法，生成100个点，每个点的取值在[-1,1]之间

y = 2x + 1 + 噪声,其中，噪声的维度与x_data一致

np.random.randn(x_data.shape)实参的前面加上和*，就意味着拆包，单个号表示将元组拆成一个个单独的实参

 x_data = np.linspace(-1, 1, 100)
 y_data = 2 * x_data + 1.0 + np.random.randn(*x_data.shape) * 0.4

利用matplotlib绘图

 ​
 plt.scatter(x_data, y_data)
 plt.show()

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 plt.plot(x_data, 2 * x_data + 1.0, color="red", linewidth=3)
 plt.show()

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定义模型

定义训练数据的占位符，x是特征值，y是标签值

 x = tf.placeholder("float", name="x")
 y = tf.placeholder("float", name="y")

定义模型函数

 def model(x, w, b):
     return tf.multiply(x, w) + b

创建变量

  • TensorFlow变量的声明函数是tf.Variable

  • tf,Variable的作用是保存和更新参数

  • 变量的初始值可以是随机数、常数，或是通过其他变量的初始值计算得到

 # 构建线性函数的斜率，变量2
 w = tf.Variable(1.0, name="w0")
 # 构建线性函数的截距，变量b
 b = tf.Variable(0.0, name="b0")
 # pred是预测值，前向计算
 pred = model(x, w, b)

模型训练

  1. 设置训练参数

train_epochs = 10  # 迭代次数
learning_rate = 0.05  # 学习率

  1. 损失函数

  • 损失函数用于描述预测值和真实值之间的误差，从而指导模型的收敛方向

  • 常见的损失函数：

    1. 均方差(Mean Square Error)

    2. 交叉熵(cross-entropy)


loss_function = tf.reduce_mean(tf.square(y - pred))  # 采用均方差

  1. 定义优化器 优化器Optimizer，初始化一个GradientDescentOPtimizer 设置学习率和优化目标：最小化损失

# 梯度下降优化器
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(
    loss_function)

创建会话,变量初始化

  • 在真正进行计算之气，需将所有变量初始化

  • 通过tf.global_variables_initializer()函数可实现对所有变量的初始化

sess = tf.Session()
init = tf.global_variables_initializer()
sess.run(init)

迭代训练

模型训练阶段，设置迭代轮次，通过将样本逐个输入模型，进行梯度优化操作。每轮迭代后，绘制出模型曲线

for epoch in range(train_epochs):
    for xs, ys in zip(x_data, y_data):
        _, loss = sess.run([optimizer, loss_function],
                           feed_dict={
                               x: xs,
                               y: ys
                           })
    b0temp = b.eval(session=sess)
    w0temp = w.eval(session=sess)
    plt.plot(x_data, w0temp * x_data + b0temp)

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打印结果

print("w:",sess.run(w))
print("b:",sess.run(b))

w: 1.9822965
b: 1.0420128

可视化

plt.scatter(x_data,y_data,label="original data")
plt.plot(x_data,x_data*sess.run(w)+sess.run(b),label="fitter line",color="r",linewidth=3)
plt.legend(loc=2)
plt.show()

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进行预测

x_test = 3.21
predict = sess.run(pred,feed_dict={x:x_test})
print(f"预测值:{predict}")
target = 3* x_test +1.0
print(f"目标值:{target}")

预测值:7.405184268951416
目标值:10.629999999999999

显示损失值

step = 0
loss_list = []
display_step = 10
for eopch in range(train_epochs):
    for xs, ys in zip(x_data, y_data):
        _, loss = sess.run([optimizer, loss_function],
                           feed_dict={
                               x: xs,
                               y: ys
                           })
        loss_list.append(loss)
        step += 1
        if step % display_step == 0:
            print(f"Train Epoch:{eopch+1}", f"Step:{step}", f"loss={loss}")
    b0temp = b.eval(session=sess)
    w0temp = w.eval(session=sess)
    plt.plot(x_data,w0temp*x_data+b0temp)

Train Epoch:1 Step:10 loss=0.03621993958950043
Train Epoch:1 Step:20 loss=0.08414854109287262
Train Epoch:1 Step:30 loss=0.00047292912495322526
Train Epoch:1 Step:40 loss=0.32646191120147705
Train Epoch:1 Step:50 loss=0.027518080547451973
Train Epoch:1 Step:60 loss=0.01023304183036089
Train Epoch:1 Step:70 loss=0.12734712660312653
Train Epoch:1 Step:80 loss=0.0010273485677316785
Train Epoch:1 Step:90 loss=0.10288805514574051
Train Epoch:1 Step:100 loss=0.048337195068597794
Train Epoch:2 Step:110 loss=0.03621993958950043
Train Epoch:2 Step:120 loss=0.08414854109287262
Train Epoch:2 Step:130 loss=0.00047292912495322526
Train Epoch:2 Step:140 loss=0.32646191120147705
Train Epoch:2 Step:150 loss=0.027518080547451973
Train Epoch:2 Step:160 loss=0.01023304183036089
Train Epoch:2 Step:170 loss=0.12734712660312653
Train Epoch:2 Step:180 loss=0.0010273485677316785
Train Epoch:2 Step:190 loss=0.10288805514574051
Train Epoch:2 Step:200 loss=0.048337195068597794
Train Epoch:3 Step:210 loss=0.03621993958950043
Train Epoch:3 Step:220 loss=0.08414854109287262
Train Epoch:3 Step:230 loss=0.00047292912495322526
Train Epoch:3 Step:240 loss=0.32646191120147705
Train Epoch:3 Step:250 loss=0.027518080547451973
Train Epoch:3 Step:260 loss=0.01023304183036089
Train Epoch:3 Step:270 loss=0.12734712660312653
Train Epoch:3 Step:280 loss=0.0010273485677316785
Train Epoch:3 Step:290 loss=0.10288805514574051
Train Epoch:3 Step:300 loss=0.048337195068597794
Train Epoch:4 Step:310 loss=0.03621993958950043
Train Epoch:4 Step:320 loss=0.08414854109287262
Train Epoch:4 Step:330 loss=0.00047292912495322526
Train Epoch:4 Step:340 loss=0.32646191120147705
Train Epoch:4 Step:350 loss=0.027518080547451973
Train Epoch:4 Step:360 loss=0.01023304183036089
Train Epoch:4 Step:370 loss=0.12734712660312653
Train Epoch:4 Step:380 loss=0.0010273485677316785
Train Epoch:4 Step:390 loss=0.10288805514574051
Train Epoch:4 Step:400 loss=0.048337195068597794
Train Epoch:5 Step:410 loss=0.03621993958950043
Train Epoch:5 Step:420 loss=0.08414854109287262
Train Epoch:5 Step:430 loss=0.00047292912495322526
Train Epoch:5 Step:440 loss=0.32646191120147705
Train Epoch:5 Step:450 loss=0.027518080547451973
Train Epoch:5 Step:460 loss=0.01023304183036089
Train Epoch:5 Step:470 loss=0.12734712660312653
Train Epoch:5 Step:480 loss=0.0010273485677316785
Train Epoch:5 Step:490 loss=0.10288805514574051
Train Epoch:5 Step:500 loss=0.048337195068597794
Train Epoch:6 Step:510 loss=0.03621993958950043
Train Epoch:6 Step:520 loss=0.08414854109287262
Train Epoch:6 Step:530 loss=0.00047292912495322526
Train Epoch:6 Step:540 loss=0.32646191120147705
Train Epoch:6 Step:550 loss=0.027518080547451973
Train Epoch:6 Step:560 loss=0.01023304183036089
Train Epoch:6 Step:570 loss=0.12734712660312653
Train Epoch:6 Step:580 loss=0.0010273485677316785
Train Epoch:6 Step:590 loss=0.10288805514574051
Train Epoch:6 Step:600 loss=0.048337195068597794
Train Epoch:7 Step:610 loss=0.03621993958950043
Train Epoch:7 Step:620 loss=0.08414854109287262
Train Epoch:7 Step:630 loss=0.00047292912495322526
Train Epoch:7 Step:640 loss=0.32646191120147705
Train Epoch:7 Step:650 loss=0.027518080547451973
Train Epoch:7 Step:660 loss=0.01023304183036089
Train Epoch:7 Step:670 loss=0.12734712660312653
Train Epoch:7 Step:680 loss=0.0010273485677316785
Train Epoch:7 Step:690 loss=0.10288805514574051
Train Epoch:7 Step:700 loss=0.048337195068597794
Train Epoch:8 Step:710 loss=0.03621993958950043
Train Epoch:8 Step:720 loss=0.08414854109287262
Train Epoch:8 Step:730 loss=0.00047292912495322526
Train Epoch:8 Step:740 loss=0.32646191120147705
Train Epoch:8 Step:750 loss=0.027518080547451973
Train Epoch:8 Step:760 loss=0.01023304183036089
Train Epoch:8 Step:770 loss=0.12734712660312653
Train Epoch:8 Step:780 loss=0.0010273485677316785
Train Epoch:8 Step:790 loss=0.10288805514574051
Train Epoch:8 Step:800 loss=0.048337195068597794
Train Epoch:9 Step:810 loss=0.03621993958950043
Train Epoch:9 Step:820 loss=0.08414854109287262
Train Epoch:9 Step:830 loss=0.00047292912495322526
Train Epoch:9 Step:840 loss=0.32646191120147705
Train Epoch:9 Step:850 loss=0.027518080547451973
Train Epoch:9 Step:860 loss=0.01023304183036089
Train Epoch:9 Step:870 loss=0.12734712660312653
Train Epoch:9 Step:880 loss=0.0010273485677316785
Train Epoch:9 Step:890 loss=0.10288805514574051
Train Epoch:9 Step:900 loss=0.048337195068597794
Train Epoch:10 Step:910 loss=0.03621993958950043
Train Epoch:10 Step:920 loss=0.08414854109287262
Train Epoch:10 Step:930 loss=0.00047292912495322526
Train Epoch:10 Step:940 loss=0.32646191120147705
Train Epoch:10 Step:950 loss=0.027518080547451973
Train Epoch:10 Step:960 loss=0.01023304183036089
Train Epoch:10 Step:970 loss=0.12734712660312653
Train Epoch:10 Step:980 loss=0.0010273485677316785
Train Epoch:10 Step:990 loss=0.10288805514574051
Train Epoch:10 Step:1000 loss=0.048337195068597794


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图形现显示话损失值

plt.plot(loss_list)

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plt.plot(loss_list,"r+")

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到这里就结束了，如果对你有帮助，欢迎点赞关注评论，你的点赞对我很重要

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TensorFlow 线性回归
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