The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation.
The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation.
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DOI：
10.7717/peerj-cs.623
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Jurman G
中科院分区：
文献类型：
--
作者：
Chicco D;Warrens MJ;Jurman G
回归分析在有监督的机器学习中占很大一部分，它包括从一组其他预测变量中预测一个连续的独立目标。二分分类和回归之间的区别在于目标范围：在二分分类中，目标只能有两个值(通常编码为0和1)，而在回归中，目标可以有多个值。即使回归分析已经在大量的机器学习研究中使用，但还没有就评估回归本身的结果的单一、统一的标准度量达成共识。许多研究使用均方误差(MSE)及其根变量(RMSE)或平均绝对误差(MAE)及其百分比变量(MAPE)。虽然这些比率很有用，但它们有一个共同的缺点：由于它们的值可以介于零和+无穷大之间，因此它们中的单个值并不能很好地说明回归相对于基本事实元素的分布的性能。在这项研究中，我们关注的是只有当基本真理组的大多数元素被正确预测时才能实际产生高分的两个比率：决定系数(也称为R平方或R2)和对称平均绝对百分比误差(SMAPE)。在展示了R2和SMAPE的数学属性之后，我们报告了R2和SMAPE在几个用例和两个真实医疗场景中的比较。我们的结果表明，决定系数(R平方)比SMAPE更具信息量和真实性，并且不存在MSE、RMSE、MAE和MAPE的可解释性限制。因此，我们建议使用R平方作为标准度量来评估任何科学领域的回归分析。
Regression analysis makes up a large part of supervised machine learning, and consists of the prediction of a continuous independent target from a set of other predictor variables. The difference between binary classification and regression is in the target range: in binary classification, the target can have only two values (usually encoded as 0 and 1), while in regression the target can have multiple values. Even if regression analysis has been employed in a huge number of machine learning studies, no consensus has been reached on a single, unified, standard metric to assess the results of the regression itself. Many studies employ the mean square error (MSE) and its rooted variant (RMSE), or the mean absolute error (MAE) and its percentage variant (MAPE). Although useful, these rates share a common drawback: since their values can range between zero and +infinity, a single value of them does not say much about the performance of the regression with respect to the distribution of the ground truth elements. In this study, we focus on two rates that actually generate a high score only if the majority of the elements of a ground truth group has been correctly predicted: the coefficient of determination (also known as R-squared or R2) and the symmetric mean absolute percentage error (SMAPE). After showing their mathematical properties, we report a comparison between R2 and SMAPE in several use cases and in two real medical scenarios. Our results demonstrate that the coefficient of determination (R-squared) is more informative and truthful than SMAPE, and does not have the interpretability limitations of MSE, RMSE, MAE and MAPE. We therefore suggest the usage of R-squared as standard metric to evaluate regression analyses in any scientific domain.
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