TensorFlow笔记之多元线性回归

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前言

记录使用TensorFlow1.x和TensorFlow2.x完成多元线性回归的过程。

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一、数据处理

在此使用波士顿房价数据集，包含506个样本，输入为12个房屋信息特征，输出为房价。
使用pandas库读取csv文件，对数据进行归一化以消除不同维度量级上的差异，进行训练集与测试集的划分以评估训练结果。

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
#数据读取
df = pd.read_csv(r'database/boston.csv', header=0)
x_data = np.array(df.values)[:,:12]
y_data = np.array(df.values)[:,12]
#数据归一化
for i in range(12):
    x_data[:,i] = x_data[:,i] / (np.max(x_data[:,i]) - np.min(x_data[:,i]))
#数据集划分
x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.3)
#维度变换
x_train = x_train.reshape((-1, 12))
x_test = x_test.reshape((-1, 12))
y_train = y_train.reshape((-1, 1))
y_test = y_test.reshape((-1, 1))

二、TensorFlow1.x

1.定义模型

import tensorflow.compat.v1 as tf
import matplotlib.pyplot as plt
from sklearn.utils import shuffle
tf.disable_eager_execution()
#使用命名空间对节点打包
with tf.name_scope('Model'):
    #创建变量
    x = tf.placeholder(tf.float32, [None, 12], name='X')
    y = tf.placeholder(tf.float32, [None, 1], name='Y')
    w = tf.Variable(tf.random.normal((12,1)), name='w')
    b = tf.Variable(tf.random.normal((1, 1)), name='b')
    def model(x, w, b):
        return tf.matmul(x, w) + b
    #预测节点
    pred = model(x, w, b)

2.训练模型

使用小批量梯度下降进行训练，每轮过后打乱训练集顺序。

#训练参数
train_epoch = 100
learning_rate = 0.01
batch_size = 100
batch_num = (x_train.shape[0] // batch_size)
#损失函数
step = 0
display_step = 5
loss_list_test = []
loss_list_train = []
with tf.name_scope('LossFunction'):
    loss_function = tf.reduce_mean(tf.square(y - pred))
#定义优化器
optimizer = tf.train.GradientDescentOptimizer(learning_rate)\
    .minimize(loss_function)
#变量初始化
sess = tf.Session()
init = tf.global_variables_initializer()
sess.run(init)

迭代训练

for epoch in range(train_epoch):
    for batch in range(batch_num):
        xi = x_train[batch * batch_size:(batch + 1) * batch_size]
        yi = y_train[batch * batch_size:(batch + 1) * batch_size]
        sess.run(optimizer, feed_dict={
    
    x:xi, y:yi})
        step = step + 1
        if step % display_step == 0:
            loss_train = sess.run(loss_function,\
                                  feed_dict={
    
    x:x_train, y:y_train})
            loss_test= sess.run(loss_function,\
                                feed_dict={
    
    x:x_test, y:y_test})
            loss_list_train.append(loss_train)
            loss_list_test.append(loss_test)
            #print('w=', sess.run(w), '\n', 'b=', sess.run(b))
	#打乱训练集顺序
    x_train, y_train = shuffle(x_train, y_train)

3.结果可视化

plt.plot(loss_list_train, 'b-')
plt.plot(loss_list_test, 'r-')
print('train_epoch=', train_epoch)
print('learning_rate', learning_rate)
print('batch_size=', batch_size)

测试集损失函数比训练集下降得更快

增大训练轮数，减少批次样本量，损失函数进一步下降

将测试集比例设置为0.99，只用5个样本作为训练集，经过数轮训练后，训练集损失函数趋于0，测试集损失函数上升，产生了过拟合。

4.模型预测

从测试集随机抽取样本进行预测

i = np.random.randint(0, 50)
print('第%i个样本：' % i)
print('预测值：', sess.run(pred, feed_dict={
    
    x:x_test[i].reshape((1, 12))}))
print('实际值：', y_test[i])
sess.close()

差距有大有小

5.TensorBoard可视化

在变量初始化后加入：

#设置存储目录
tf.reset_default_graph()
log_dir = 'G://log'
#记录损失值
sum_loss_op = tf.summary.scalar('loss', loss_function)
#合并写入
merged = tf.summary.merge_all()
#文件写入器
write = tf.summary.FileWriter(log_dir, sess.graph)

将损失值加入摘要：

loss_train, sum_loss = sess.run([loss_function, sum_loss_op],\
                                  feed_dict={
    
    x:x_train, y:y_train})
write.add_summary(sum_loss, epoch)

关闭：

write.close()

在Anaconda Prompt中进入日志目录，运行TensorBoard，访问网址。
可以看到损失值和计算图

三、TensorFlow2.x

1.定义模型

import tensorflow as tf
import matplotlib.pyplot as plt

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

def loss_function(x, y, w, b):
    pred = model(x, w, b)
    loss = tf.reduce_mean(tf.square(y - pred))
    return loss

def grad(x, y, w, b):
    with tf.GradientTape() as tape:
        loss = loss_function(x, y, w, b)
    return tape.gradient(loss, [w, b])

w = tf.Variable(tf.random.normal((12,1)), dtype=tf.float32)
b = tf.Variable(tf.random.normal((1,1)), dtype=tf.float32)

矩阵乘法需要转化为Tensor

x_train = tf.cast(x_train, tf.float32)
x_test = tf.cast(x_test, tf.float32)
y_train = tf.cast(y_train, tf.float32)
y_test = tf.cast(y_test, tf.float32)

2.训练模型

#训练参数
train_epoch = 100
learning_rate = 0.01
batch_size = 100
batch_num = x_train.shape[0] // batch_size
step = 0
display_step = 5
loss_list_train = []
loss_list_test = []
#创建优化器
optimizer = tf.keras.optimizers.SGD(learning_rate)

迭代训练

for epoch in range(train_epoch):
    for batch in range(batch_num):
        xi = x_train[batch*batch_size : (batch+1)*batch_size]
        yi = y_train[batch*batch_size : (batch+1)*batch_size]
        grads = grad(xi, yi, w, b)
        #应用梯度
        optimizer.apply_gradients(zip(grads, [w,b]))
        step = step + 1
        if step % display_step == 0:
            loss_list_train.append(loss_function(x_train, y_train, w, b))
            loss_list_test.append(loss_function(x_test, y_test, w, b))
    #使用tf.random.shuffle打乱Tensor类型的数据集
    train_data = tf.concat([x_train, y_train], axis=1)
    train_data = tf.random.shuffle(train_data)
    x_train = train_data[:, :12]
    y_train = tf.reshape(train_data[:, 12], (-1,1))

3.结果可视化

plt.plot(loss_list_train, 'b-')
plt.plot(loss_list_test, 'r-')
print('train_epoch=', train_epoch)
print('learning_rate', learning_rate)
print('batch_size=', batch_size) 

4.模型预测

i = np.random.randint(0, 50)
pred = model(tf.reshape(x_test[i], (1,12)), w, b).numpy()
print('第%i个样本：' % i)
print('预测值：', pred)
print('实际值：', y_test[i].numpy()) 

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总结

TensorFlow1.x与TensorFlow2.x部分语法存在差异，使用TensorBoard进行展示时需要将之前的log文件删除；进行矩阵乘法时，需要注意数据类型与维度；由于数据集较小，采用的是线性回归，模型的准确程度有待优化。