Root mean square error (RMSE) or mean absolute error (MAE)? - Arguments against avoiding RMSE in the literature
Root mean square error (RMSE) or mean absolute error (MAE)? - Arguments against avoiding RMSE in the literature
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DOI：
10.5194/gmd-7-1247-2014
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发表时间：
2014-01-01
影响因子：
5.1
通讯作者：
Draxler, R. R.
中科院分区：
文献类型：
--
作者：
Chai, T.;Draxler, R. R.
均方根误差(RMSE)和平均绝对误差(MAE)通常用于模型评估研究。Willmott和Matsuura(2005)提出，RMSE不是衡量平均模型性能的良好指标，而可能是衡量平均误差的误导性指标，因此MAE将是一个更好的衡量标准。尽管Willmott和Matsuura(2005)和Willmott等人对使用RMSE提出了一些担忧。(2009)是有效的，建议避免RMSE而支持MAE不是解决办法。引用上述论文，许多研究人员选择MAE而不是RMSE来展示他们的模型评估统计数据，因为展示或添加RMSE措施可能更有益。在这份技术说明中，我们证明了RMSE的含义并不含糊，这与Willmott等人的说法相反。(2009)。当误差分布为高斯分布时，RMSE比MAE更适合表示模型性能。此外，我们还证明了RMSE满足距离度量的三角不等要求，而Willmott等人则证明了RMSE满足距离度量的三角不等式要求。(2009)指出，基于平方和的统计数据不符合这一规则。最后，我们讨论了使用RMSE会更有利的一些情况。然而，我们并不认为RMSE优于MAE。取而代之的是，评估模型的性能通常需要一系列指标的组合，包括但当然不限于RMSE和MAE。
Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.