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数据拟合上课学生代码.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jun 13 06:23:11 2021
+
+@author: hzh
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+# 生成100个数据点
+np.random.seed(7)
+X = 2 * np.random.rand(100)  # 生成100个随机数，模拟x
+Y = 15 + 3 * X + np.random.randn(100)  # 生成100个随机数，模拟y，真实的a=3,b=15
+fig, ax = plt.subplots()
+ax.scatter(X, Y)
+fig.savefig('scatter.pdf')
+fig.show()
+
+learning_rate = 0.1
+roundN = 7  # 对数据点集的轮数
+np.random.seed(3)
+a = np.random.randn()
+b = np.random.randn()
+print(a)
+print(b)
+
+
+# 函数定义求误差的最小值
+def errorCompute(a, b):
+	error = 0
+	for j in range(len(X)):
+		error += 1 / 2 * (a * X[j] + b - Y[j]) ** 2
+	return error / len(X)
+
+
+# 用梯度下降法求得a,b的值
+# 通过多轮迭代，输出每轮迭代的误差，当误差的变化不大的时候此时的a,b为所求的拟合线的值
+for i in range(roundN):
+	for j in range(len(X)):
+		if j % 50 == 0:
+			print("round=%d,iter=%d,a=%f,b=%f,E=%f" % (i, j, a, b, errorCompute(a, b)))
+		gradA = (a * X[j] + b - Y[j]) * X[j]  # 对a求偏导的公式
+		gradB = a * X[j] + b - Y[j]  # 对b求偏导的公式
+		a = a - learning_rate * gradA  # 迭代公式
+		b = b - learning_rate * gradB  # 迭代公式
+print(a, b)  # 输出a,b的值
+# 下面绘制图形
+maxX = max(X)
+minX = min(X)
+maxY = max(Y)
+minY = min(Y)
+X_fit = np.arange(minX, maxX, 0.01)
+Y_fit = a * X_fit + b  # 梯度下降法得到的拟合线的方程
+plt.plot(X, Y, '.')  # 散点图100个点
+plt.plot(X_fit, Y_fit, 'r-', label='Gradient Descent')  # 拟合线
+plt.plot(X_fit, 15 + 3 * X_fit, 'b-', label='True')  # 实际的线
+plt.legend()  # 显示图例
+plt.show()
+
+# 练习题：
+#################begin##################
+# 模拟函数y=10x+30,生成100个数据点坐标。
+# 请用梯度下降法拟合出数据点隐含的线性函数y=ax+b，求出a,b值。
+
+
+# 数据拟合2
+# 模拟二元函数f(x,y)=5*x+10*y+30,生成1000个数据点坐标。
+# 用梯度下降法拟合出数据点隐含的线性函数f(x,y)=w1*x+w2*y+b的
+# w1,w2,b值
+
+
+# 线性预测
+import numpy as np
+from sklearn.model_selection import train_test_split
+
+# 数据处理
+data = np.loadtxt('advertising.txt', delimiter=',')
+print(data)
+X = data[:, 0:-1]
+y = data[:, -1]
+X = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))  # 归一化处理
+# print(X)
+# 分割训练与测试
+X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)
+# 梯度下降法，y=w1*x1+w2*x2+w3*x3+b
+# 初始化
+np.random.seed(10)
+w1, w2, w3, w4, b = np.random.randn(5)
+lr = 0.001  # 0.00001
+rounds = 1000  # 300,0.001 ,4.54
+
+
+def computeErr(X, y):  # 误差计算
+	err = 0
+	for i in range(len(X)):
+		err += 1 / 2 * (X[i, 0] * w1 + X[i, 1] * w2 + X[i, 2] * w3 + b - y[i]) ** 2
+	return err / len(X)
+
+
+for i in range(rounds):  # 梯度下降法拟合训练集
+	for j in range(len(X_train)):
+		w1 -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j]) * X_train[j, 0]
+		w2 -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j]) * X_train[j, 1]
+		w3 -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j]) * X_train[j, 2]
+		b -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j])
+	if i % 100 == 0:
+		print('第%i轮迭代训练集误差=%.2f' % (i, computeErr(X_train, y_train)))
+# 模型评估
+print('测试集误差：', computeErr(X_test, y_test))
+print('权重：', w1, w2, w3)
+print('截距：', b)
+predict = (X_test * np.array([w1, w2, w3])).sum(axis=1) + b
+print(len(predict))
+mse = ((predict - y_test) ** 2).sum() / len(y_test)
+print('rmse=', mse ** 0.5)