回归预测评估指标

青旅半醒 2022-05-27 09:16 213阅读 0赞

### 标注说明 ###

ff表示预测值，yy表示实际值

### 评价指标 ###

*  MAE(Mean Absolute Error) 平均绝对误差   
    
    
    MAE=1n∑i=1n|fi−yi|MAE=1n∑i=1n|fi−yi|
 *  MSE(Mean Square Error) 平均平方差/均方误差是回归任务最常用的性能度量。   
    
    
    MSE=1n∑i=1n(fi−yi)2MSE=1n∑i=1n(fi−yi)2
 *  [RMSE(Root Mean Square Error)][RMSE_Root Mean Square Error] 方均根差   
    
    
    RMSE=MSE−−−−−√RMSE=MSE
    
      
    缺点：因为它使用的是平均误差，而平均误差对异常点较敏感，如果回归器对某个点的回归值很不合理，那么它的误差则比较大，从而会对RMSE的值有较大影响，即平均值是非鲁棒的。
 *  MAPE   
    全称是Mean Absolute Percentage Error（[WikiPedia][]）, 也叫mean absolute percentage deviation (MAPD)，在统计领域是一个预测准确性的衡量指标。   
    
    
    MAPE=100n∑t=1n|yi−fiyi|MAPE=100n∑t=1n|yi−fiyi|
 *  R平方   
    y¯y¯表示观测数据的平均值   
    残差平方和   
    
    
    SSres=∑(yi−fi)2SSres=∑(yi−fi)2
    
      
    总平均值   
    
    
    SStot=∑(yi−y¯)2SStot=∑(yi−y¯)2
    
      
    R平方   
    
    
    r2=1−SSresSStot=1−∑(yi−fi)2∑(yi−y¯)2r2=1−SSresSStot=1−∑(yi−fi)2∑(yi−y¯)2
    
      
    R平方是多元回归中的回归平方和占总平方和的比例,它是度量多元回归方程中拟合程度的一个统计量,反映了在因变量yy的变差中被估计的回归方程所解释的比例。   
    R平方越接近1,表明回归平方和占总平方和的比例越大,回归线与各观测点越接近,用xx的变化来解释yy值变差的部分就越多,回归的拟合程度就越好。
 *  校正R平方   
    [http://www.statisticshowto.com/adjusted-r2/][http_www.statisticshowto.com_adjusted-r2]   
    ![这里写图片描述][SouthEast]
    
    > where: N is the number of points in your data sample.   
    > K is the number of independent regressors, i.e. the number of variables in your model, excluding the constant
 *  RMSPE   
    
    
    RMSPE=1n∑i=1n(yi−y^iyi)2−−−−−−−−−−−−−−−⎷RMSPE=1n∑i=1n(yi−y^iyi)2
    
      
    where yiyi denotes the sales of a single store on a single day and y^iy^i denotes the corresponding prediction.

[https://www.kaggle.com/cast42/xgboost-in-python-with-rmspe-v2/code][https_www.kaggle.com_cast42_xgboost-in-python-with-rmspe-v2_code]

*  RMSLE(Root Mean Squared Logarithmic Error) Kaggle 上用的一个指标[https://www.kaggle.com/wiki/RootMeanSquaredLogarithmicError][https_www.kaggle.com_wiki_RootMeanSquaredLogarithmicError]

def rmsle(predicted,real):
        sum=0.0
        for x in range(len(predicted)):
            p = np.log(predicted[x]+1)
            r = np.log(real[x]+1)
            sum = sum + (p - r)**2
        return (sum/len(predicted))**0.5

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# https://www.kaggle.com/jpopham91/rmlse-vectorized
    # vectorized error calc
    def rmsle(y, y0):
        assert len(y) == len(y0)
        return np.sqrt(np.mean(np.power(np.log1p(y)-np.log1p(y0), 2)))

[RMSE_Root Mean Square Error]: https://en.wikipedia.org/wiki/Root-mean-square_deviation
[WikiPedia]: https://en.wikipedia.org/wiki/Mean_absolute_percentage_error
[http_www.statisticshowto.com_adjusted-r2]: http://www.statisticshowto.com/adjusted-r2/
[SouthEast]: /images/20220527/84b49bb48a2b4d039479170663ce8a60.png
[https_www.kaggle.com_cast42_xgboost-in-python-with-rmspe-v2_code]: https://www.kaggle.com/cast42/xgboost-in-python-with-rmspe-v2/code
[https_www.kaggle.com_wiki_RootMeanSquaredLogarithmicError]: https://www.kaggle.com/wiki/RootMeanSquaredLogarithmicError