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RMSE vs MAE — how do you pick?

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Answer

  • RMSE = sqrt(mean((y  −  yhat)2)\mathrm{mean}((y\; - \;y_{\mathrm{hat}})2)) — same units as y, penalizes large errors quadratically.
  • Use when big errors are disproportionately bad (financial forecasting, energy grids) or when errors are approximately Gaussian.
  • MAE⁡  =  mean(∣y  −  yhat∣)\operatorname{MAE}\; = \;\mathrm{mean}( \mid y\; - \;y_{\mathrm{hat}} \mid ) — robust to outliers, more interpretable ('average error is X units'), the L1 relative of RMSE.
  • RMSE ≥ MAE always; the gap grows with error variance.
  • If a few large errors would dominate, prefer MAE (or Huber).
Check yourself — multiple choice
  • RMSE is always smaller than MAE
  • RMSE penalizes large errors more; MAE is robust to outliers and easier to explain
  • Both are identical
  • MAE is only for classification

RMSE = quadratic (large errors bite); MAE = L1 (robust). RMSE ≥ MAE always.

#metrics-regression

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