Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not

Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not

19 July 2022 | Timothy O. Hodson
The article discusses the root-mean-square error (RMSE) and mean absolute error (MAE) as widely used metrics for evaluating models. Despite their popularity, there is ongoing confusion over which metric to use, leading to the common practice of presenting both and leaving the decision to the reader. The author reviews the historical debate and provides a theoretical foundation for choosing between RMSE and MAE based on the probability distribution of errors. RMSE is optimal for normally distributed errors, while MAE is optimal for Laplacian errors. For errors that deviate from these distributions, other metrics are more suitable. The article also explores alternative methods such as refining the model structure, transforming data, using robust statistics, and constructing likelihood functions. It concludes that while RMSE and MAE are optimal in their correct applications, practical situations often require a combination of these metrics or other approaches to achieve better results.The article discusses the root-mean-square error (RMSE) and mean absolute error (MAE) as widely used metrics for evaluating models. Despite their popularity, there is ongoing confusion over which metric to use, leading to the common practice of presenting both and leaving the decision to the reader. The author reviews the historical debate and provides a theoretical foundation for choosing between RMSE and MAE based on the probability distribution of errors. RMSE is optimal for normally distributed errors, while MAE is optimal for Laplacian errors. For errors that deviate from these distributions, other metrics are more suitable. The article also explores alternative methods such as refining the model structure, transforming data, using robust statistics, and constructing likelihood functions. It concludes that while RMSE and MAE are optimal in their correct applications, practical situations often require a combination of these metrics or other approaches to achieve better results.
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