DataWhale初级算法梳理—Task02：线性回归

在这里插入图片描述

生成数据：

#生成数据
import numpy as np
#生成随机数
np.random.seed(1234)
x = np.random.rand(500,3)
#构建映射关系，模拟真实的数据待预测值,映射关系为y = 4.2 + 5.7*x1 + 10.8*x2，可自行设置值进行尝试
y = x.dot(np.array([4.2,5.7,10.8]))

1、调用sklearn的线性回归模型训练数据：

import numpy as np
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt
%matplotlib inline

# 调用模型
lr = LinearRegression(fit_intercept=True)
# 训练模型
lr.fit(x,y)
print("估计的参数值为：%s" %(lr.coef_))
# 计算R平方
print('R2:%s' %(lr.score(x,y)))
# 任意设定变量，预测目标值
x_test = np.array([2,4,5]).reshape(1,-1)
y_hat = lr.predict(x_test)
print("预测值为: %s" %(y_hat))

估计的参数值为：[ 4.2 5.7 10.8]
R2:1.0
预测值为: [85.2]

2、最小二乘法的矩阵求解：

class LR_LS():
    def __init__(self):
        self.w = None      
    def fit(self, X, y):
        # 最小二乘法矩阵求解
        temp0 = np.dot(X.T,X)
        temp = np.dot(np.linalg.inv(tempo),X.T)
        self.w = np.dot(temp,y)
        return self.w
    def predict(self, X):
        # 用已经拟合的参数值预测新自变量
        y_pred = np.dot(X,self.w)
        return y_pred

if __name__ == "__main__":
    lr_ls = LR_LS()
    lr_ls.fit(x,y)
    print("估计的参数值：%s" %(lr_ls.w))
    x_test = np.array([2,4,5]).reshape(1,-1)
    print("预测值为: %s" %(lr_ls.predict(x_test)))

估计的参数值：[ 4.2 5.7 10.8]
预测值为: [85.2]

3、梯度下降法：

class LR_GD():
    def __init__(self):
        self.w = None     
    def fit(self,X,y,alpha=0.02,loss = 1e-10): # 设定步长为0.002,判断是否收敛的条件为1e-10
        y = y.reshape(-1,1) #重塑y值的维度以便矩阵运算
        [m,d] = np.shape(X) #自变量的维度
        self.w = np.zeros((d)).reshape(d,1)#将参数的初始值定为0
        tol = 1e5
        while tol > loss:
            temp = X.dot(self.w)-y
            self.w = self.w-1/m*alpha*(temp.dot(X))
            tol = np.abs(np.sum(temp))
    def predict(self, X):
        # 用已经拟合的参数值预测新自变量
        y_pred = X.dot(self.w)
        return y_pred  
        
if __name__ == "__main__":
    lr_gd = LR_GD()
    lr_gd.fit(x,y)
    print("估计的参数值为：%s" %(lr_gd.w))
    x_test = np.array([2,4,5]).reshape(1,-1)
    print("预测值为：%s" %(lr_gd.predict(x_test)))

估计的参数值为：[ 4.20000001 5.70000003 10.79999997]
预测值为：[85.19999995]

学习资料来源：https://github.com/datawhalechina/team-learning/blob/master/%E5%88%9D%E7%BA%A7%E7%AE%97%E6%B3%95%E6%A2%B3%E7%90%86/Task2_Linear_regression.ipynb

来源：CSDN

作者：大丸子哟

链接：https://blog.csdn.net/Dawanz/article/details/103940972

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