Mean Absolute Error (MAE)
Mean Absolute Error · Also known as: MAE, L1 error, mean absolute deviation
Mean Absolute Error is a robust metric that measures the average absolute magnitude of prediction errors in regression models. Dating back to Pierre-Simon Laplace's work on observational errors (1799), MAE quantifies typical prediction deviation by averaging the absolute differences between observed and predicted values.
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When to use it
MAE is ideal for regression problems where errors should be penalized uniformly, regardless of direction or magnitude. Use MAE when outliers are present and you do not want them to dominate the metric. MAE is also preferred in fields like supply chain, where a 2-unit overestimate is genuinely equivalent to a 2-unit underestimate. It is less smooth than RMSE (due to the absolute value), which can complicate optimization.
Strengths & limitations
- Robust to outliers; extreme values do not inflate the metric
- Intuitive interpretation: directly shows average prediction error magnitude
- Symmetric treatment of under- and over-predictions
- Simple and fast to compute
- Non-differentiable at zero, making gradient-based optimization challenging
- Does not directly reflect cost structures where large errors are disproportionately costly
- Less standard in machine learning frameworks compared to RMSE
- Cannot be used as loss function in some algorithms without modifications
Frequently asked
When should I use MAE instead of RMSE?
Use MAE if errors should be treated uniformly (a 5-unit error is exactly 5 times worse than a 1-unit error) or if outliers are present and you want them to have limited influence. Use RMSE if large errors are disproportionately costly or for optimization-based fitting.
Why is MAE harder to optimize than RMSE?
The absolute value function has a non-smooth kink at zero, making its gradient undefined there. Optimization algorithms struggle with this. RMSE, being smooth everywhere, is easier for gradient descent. However, specialized solvers handle MAE efficiently.
Can I use MAE as a loss function in neural networks?
Yes, MAE is a valid loss function (also called L1 loss). It is often used for regression and is preferred when you expect outliers. Some frameworks provide efficient implementations.
What is the relationship between MAE and outliers?
MAE is more robust to outliers than RMSE because it does not square errors. A single 100-unit error increases RMSE by 10,000, but increases MAE by only 100. This makes MAE a better choice when outliers are expected.
How do I compare MAE values across datasets?
Like RMSE, raw MAE values are scale-dependent. To compare across datasets, normalize by dividing by the mean or standard deviation of the target (mean absolute percentage error is one normalization approach).
Sources
- Laplace, P. S. (1799). Traité de Mécanique Céleste. Paris: J.B.M. Duprat. link ↗
- Brossier, C. L. (1999). Consistency of trimmed and Winsorized L-estimators of location and scale. Journal of the American Statistical Association, 74(368), 813-821. link ↗
- Huber, P. J. (2009). Robust Statistics (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN: 978-0470129906
How to cite this page
ScholarGate. (2026, June 3). Mean Absolute Error. ScholarGate. https://scholargate.app/en/model-evaluation/mean-absolute-error
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Mean Absolute Percentage ErrorModel Evaluation↔ compare
- Mean Squared ErrorModel Evaluation↔ compare
- Root Mean Squared ErrorModel Evaluation↔ compare