线性回归算法-2.简单线性回归的实现

分手后的思念是犯贱 2023-08-17 16:44 159阅读 0赞

# 线性回归算法的实现 #

import numpy
    import matplotlib.pyplot as plt
    # 使用自己模拟的简单数据集
    x = numpy.array([1,2,3,4,5])
    y = numpy.array([1,3,2,3,5])
    plt.scatter(x,y)
    plt.axis([0,6,0,6])
    plt.show()

![1465169-20190714130742235-1211153211.png][]

**线性回归算法核心，求a,b的值：**  
![1465169-20190714130803154-815439552.png][]

# 求数据集的平均数
    x_mean = numpy.mean(x)
    y_mean = numpy.mean(y)
    # 求a和b的值
    m = 0
    z = 0
    #此处计算效率太低，后续需要进行向量化
    for x_i,y_i in zip(x,y):
        z += (x_i-x_mean)*(y_i-y_mean)
        m += (x_i-x_mean)**2      
    a = z/m
    b = y_mean - a*x_mean

![1465169-20190714130819065-502763211.png][]

y_hat = a*x+b
    plt.scatter(x,y)
    plt.plot(x,y_hat,color='r')
    plt.axis([0,6,0,6])
    plt.show()

![1465169-20190714130831857-1308256397.png][]

###  调用自己封装的库 ###

调用SimpleLineRegression库

from mylib.SimpleLineRegression import SimpleLineRegression 
    reg1 = SimpleLineRegression()
    reg1.fit(x,y)
    reg1.predict(numpy.array([6]))

![1465169-20190714130843808-66419954.png][]

## 向量化 ##

a值计算时采用for循环，效率较低，观察a的表达式发现，可以用向量间的点乘实现：  
![1465169-20190714130859386-2002818156.png][]

实现：

z = (x_train-x_mean).dot(y_train-y_mean)
    m = (x_train-x_mean).dot(x_train-x_mean)     
    a = z/m
    b = y_mean - a*x_mean

### 性能比较 ###

# 用随机数生成100万个样本
    m = 1000000
    big_x = numpy.random.random(size=m)
    # 模拟线性回归 a=2,b=3，构造y=ax+b,每个样本加入正态分布的干扰
    big_y = 2.0*big_x + 3.0 + numpy.random.normal(size=m)
    
    from mylib.SimpleLineRegression import SimpleLineRegression_1,SimpleLineRegression_2
    reg1 = SimpleLineRegression_1()
    reg2 = SimpleLineRegression_2()
    
    %timeit reg1.fit(big_x,big_y) # for循环
    %timeit reg2.fit(big_x,big_y) # 向量化

由下图可以看出，向量化运算比简单的for循环要快100倍

![1465169-20190714131406894-79848350.png][]

转载于:https://www.cnblogs.com/shuai-long/p/11183977.html

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[1465169-20190714130803154-815439552.png]: /images/20230809/159d8824c45d47b8b08ab1d7e03b0127.png
[1465169-20190714130819065-502763211.png]: /images/20230809/01332331ec3444f585d83d191a5bafb0.png
[1465169-20190714130831857-1308256397.png]: /images/20230809/86200736a8a447809407a26028feb999.png
[1465169-20190714130843808-66419954.png]: /images/20230809/7eb1ca6e07234d798942fa6442fbd486.png
[1465169-20190714130859386-2002818156.png]: /images/20230809/b2e1ada9b3654e82b5b9f7bd78057446.png
[1465169-20190714131406894-79848350.png]: /images/20230809/4dbfa372cce94aaca03161a5a261a7a8.png