神经网络与深度学习——TensorFlow2.0（多元线性回归模型）

使用波士顿房价数据集中的所有属性，训练和测试多元线性回归模型，并可视化模型。

要求：程序+文本（记录下超参数的调试过程，并简要总结）

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

boston_housing = tf.keras.datasets.boston_housing
(train_x, train_y), (test_x, test_y) = boston_housing.load_data()

num_train = len(train_x)
num_test = len(test_x)

x_train = (train_x - train_x.min(axis=0)) / (train_x.max(axis=0) - train_x.min(axis=0))
y_train = train_y

x_test = (test_x - test_x.min(axis=0)) / (test_x.max(axis=0) - test_x.min(axis=0))
y_test = test_y

x0_train = np.ones(num_train).reshape(-1, 1)
x0_test = np.ones(num_test).reshape(-1, 1)

X_train = tf.cast(tf.concat([x0_train, x_train], axis=1), tf.float32)
X_test = tf.cast(tf.concat([x0_test, x_test], axis=1), tf.float32)

Y_train = tf.constant(y_train.reshape(-1, 1), tf.float32)
Y_test = tf.constant(y_test.reshape(-1, 1), tf.float32)

#设置超参数
learn_rate = 0.01  # 学习率
iter = 2000  # 迭代次数
display_step = 200  # 显示间隔

#设置模型变量初始值
np.random.seed(612)
W = tf.Variable(np.random.randn(14,1),dtype=tf.float32)

mse_train = []  # 训练损失，训练误差
mse_test = []  # 测试损失，测试误差

for i in range(0 , iter+1):

   with tf.GradientTape() as tape:

       PRED_train = tf.matmul(X_train, W)
       Loss_train = 0.5 * tf.reduce_mean(tf.square(Y_train - PRED_train))

       PRED_test = tf.matmul(X_test, W)
       Loss_test = 0.5 * tf.reduce_mean(tf.square(Y_test - PRED_test))

   mse_train.append(Loss_train)
   mse_test.append(Loss_test)

   dL_dW = tape.gradient(Loss_train,W)
   W.assign_sub(learn_rate * dL_dW)
   # 输出训练误差和测试误差
   if i % display_step == 0:
       print("i:%i,Train Loss: %f, Test Loss: %f" % (i, Loss_train, Loss_test))
   # 绘图
plt.figure(figsize=(20, 4))

plt.subplot(131)
plt.ylabel("MSE")
plt.plot(mse_test, color="blue", linewidth="3", label="train loss")
plt.plot(mse_test, color="red", linewidth="1.5", label="test loss")

plt.subplot(132)
plt.plot(y_train, color="blue", marker="o", label="true_price")
plt.plot(PRED_train, color="red", marker=".", label="predict")
plt.legend()
plt.ylabel("Price")

plt.subplot(133)
plt.plot(y_test, color="blue", marker="o", label="true_price")
plt.plot(PRED_test, color="red", marker=".", label="predict")
plt.legend()
plt.ylabel("Price")

plt.show()