线性回归算法-3.线性回归算法的衡量标准

喜欢ヅ旅行 2023-08-17 16:44 108阅读 0赞

# 线性回归算法的衡量标准 #

*  **均方误差（Mean Squared Error）**

\\\[\\frac\{1\}\{m\}\\sum\_\{i=1\}^\{m\}(y\_\{test\}^\{(i)\}- \\hat y\{\_\{test\}^\{(i)\}\})^2\\\]

*  **均方根误差（Root Mean Squared Error）**  
    \\\[\\sqrt\{\\frac\{1\}\{m\}\\sum\_\{i=1\}^\{m\}(y\_\{test\}^\{(i)\}- \\hat y\{\_\{test\}^\{(i)\}\})^2\}\\\]
 *  **平均绝对误差（Mean Absolute Error）**  
    \\\[\\frac\{1\}\{m\}\\sum\_\{i=1\}^\{m\} \\left | (y\_\{test\}^\{(i)\}- \\hat y\{\_\{test\}^\{(i)\}\}) \\right| \\\]

***加载波士顿房产数据***

import numpy
    import matplotlib.pyplot as plt
    from sklearn import datasets
    
    boston = datasets.load_boston()
    # 打印此数据集的描述
    print(boston.DESCR)

![1465169-20190714175956139-1414432332.png][]

x = boston.data[:,5] #只取房间数量这个特征

![1465169-20190714180007997-995621320.png][]

plt.scatter(x,y)
    plt.show()

![1465169-20190714180022839-815059325.png][]

存在边缘极值点，用numpy中的"fancy index"去除数据中的上限值

x = x[y<50]
    y = y[y<50]
    plt.scatter(x,y)
    plt.show()

![1465169-20190714180033534-1167828998.png][]

from mylib.model_selection import train_test_split
    from mylib.SimpleLineRegression import SimpleLineRegression
    
    x_train,x_test,y_train,y_test = train_test_split(x,y,seed =666)
    reg = SimpleLineRegression()
    reg.fit(x_train,y_train)
    y_predict = reg.predict(x_test)

通过训练，得到了a,b两个参数，从而确定了线性方程  
![1465169-20190714180048042-721142438.png][]

plt.scatter(x,y)
    plt.plot(x,reg.predict(x))
    plt.show()

![1465169-20190714180103973-1609458394.png][]

**MSE 均方误差**

mse_test = numpy.sum((y_predict-y_test)**2) / len(x_test)

**RMSE 均方根误差**

import math
    mse_test = numpy.sum((y_predict-y_test)**2) / len(x_test)
    rmse_test = math.sqrt(mse_test)

**MAE 平均绝对误差**

mae_test = numpy.sum(numpy.absolute(y_predict-y_test)) / len(x_test) #absolute 求绝对值

### 上述算法指标封装为库： ###

metrics文件：  
![1465169-20190714180120103-459070007.png][]

调用封装的算法度量库：

from mylib.metrics import mean_squared_error,root_mean_squared_error,mean_absolute_error
    
    mean_squared_error(y_predict,y_test)
    root_mean_squared_error(y_predict,y_test)
    mean_absolute_error(y_predict,y_test)

![1465169-20190714180956425-1345831393.png][]

### sk-learn 中的MSE和MAE调用： ###

from sklearn.metrics import mean_squared_error,mean_absolute_error
    
    mean_squared_error(y_predict,y_test)
    mean_absolute_error(y_predict,y_test)

## R Squared ##

**表达式为: $ R^2 = 1 - \\frac\{\\Sigma(\\hat\{y\}^\{(i)\} - y^\{(i)\})^2\}\{\\Sigma(\\overline\{y\}^\{(i)\} - y^\{(i)\})^2 \} = 1 - \\frac\{MSE(\\hat\{y\},y)\}\{Var(y)\} $**

*  $ \\Sigma(\\hat\{y\}^\{(i)\} - y^\{(i)\})^2 = SS\_\{residual\} $ 使用得到的模型预测产生的错误  
    
 *  $ \\Sigma(\\overline\{y\}^\{(i)\} - y^\{(i)\})^2 = SS\_\{total\} $ 使用\$y=\\hat\{y\}\$预测产生的错误（baseline Model）  
    ![1465169-20190714180137240-732874039.png][]

# var求方差
    R2 = 1 - mean_squared_error(y_test,y_predict)/numpy.var(y_test)

封装到mylib中的metrics库中

from mylib.metrics import r2_score
    r2_score(y_test,y_predict)
    
    # 在线性回归类中封装score方法
    reg.score(x_test,y_test)

转载于:https://www.cnblogs.com/shuai-long/p/11185059.html

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[1465169-20190714180007997-995621320.png]: /images/20230809/a3d204dfc50b43e7a92b341b751845e2.png
[1465169-20190714180022839-815059325.png]: /images/20230809/9a63bea6762e4c729cd73285024f011d.png
[1465169-20190714180033534-1167828998.png]: /images/20230809/a4af650c80ec4491b2c71f33b3f41ba4.png
[1465169-20190714180048042-721142438.png]: /images/20230809/b767aec893724befb363783627785255.png
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[1465169-20190714180956425-1345831393.png]: /images/20230809/cdd20af140044376bca57a39e571a791.png
[1465169-20190714180137240-732874039.png]: /images/20230809/a74537ead519493db5e8ed44010daf0d.png