python_误差分析_python做误差分析

python_误差分析

简介

在机器学习中，MSE和MAE是常用的评价回归模型的指标。
MSE(Mean Squared Error)均方误差，预测值与真实值之差的平方和的平均值：

MAE(Mean Absolute Error) 平均绝对误差：

计算过程

目标变量

target = [ -2.2, 0.1, -0.5,0.5, 1.5, 2.1]
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预测结果

prediction = [ -4.7, -2.3, 0.75,1.5, 2.1, 3.3]
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计算误差error

error = []
for i in range(len(target)):
    error.append(target[i] - prediction[i])
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结果：

[2.5, 2.4, -1.25, -1.0, -0.6，-1.19]
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计算误差squaredError和absError

squaredError = []
absError = []
for val in error:
    squaredError.append(val * val)#target-prediction之差平方 
    absError.append(abs(val))#误差绝对值
print("Square Error[误差平方]）: ", squaredError)
print("Absolute Value of Error[误差绝对值]: ", absError) 
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结果：

Square Error[误差平方]：[6.25, 5.76, 1.5625, 1.0, 0.36, 1.4399]
Absolute Value of Error[误差绝对值]:  [2.5, 2.4, 1.25, 1.0, 0.6, 1.199]
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计算误差均方误差MSE

print( sum(squaredError))
print( len(squaredError))
print("MSE = ", sum(squaredError) / len(squaredError)) #均方误差MSE
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结果：

sum(squaredError)：16.3725
len(squaredError)：6
MSE =  2.72875
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计算误差平均绝对误差MAE

from math import sqrt
print("RMSE = ", sqrt(sum(squaredError) / len(squaredError)))#均方根误差RMSE
print("MAE = ", sum(absError) / len(absError))#平均绝对误差MAE
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结果：

RMSE =  1.65
MAE =  1.49
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计算误差方差和标准差
方差，是样本实际值与实际值的总体平均值之差的平方和的平均值，描述数据集的离散程度。
方差：

标准差：

targetDeviation = []
targetMean = sum(target) / len(target)  # target平均值
for val in target:
    targetDeviation.append((val - targetMean) * (val - targetMean))
print("Target Variance = ", sum(targetDeviation) / len(targetDeviation))  # 方差
print("Target Standard Deviation = ", sqrt(sum(targetDeviation) / len(targetDeviation)))  # 标准差
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结果：

Target Variance[方差] =  1.939
Target Standard Deviation[标准差] =  1.39
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补充：平均相对误差
https://www.jianshu.com/p/705fdb11ccd5
https://blog.csdn.net/reallocing1/article/details/56292877
参考：[https://blog.csdn.net/stone_fall/article/details/89389269]
[https://blog.csdn.net/llx1026/article/details/77752121?yyue=a21bo.50862.201879]
[https://blog.csdn.net/xiongchengluo1129/article/details/79155550]
http://latex.codecogs.com/eqneditor/editor.php