MAE (Mean Absolute Error)
Last Updated: July 29, 2026 | By Mihail Sebastian | AI Dictionary
The average absolute difference between predicted and actual values: a regression loss that weighs every error in proportion and resists outliers.
What is MAE (Mean Absolute Error)?
MAE (mean absolute error) is a regression loss that averages the absolute differences between a model’s predictions and the actual values. Every unit of error counts the same, so one extreme miss cannot dominate the score.
Its second virtue is readability: MAE stays in the target’s own units. An MAE of 2 minutes on arrival-time predictions means the model is off by 2 minutes on average, a number anyone can act on. For classification tasks, cross-entropy loss plays the role MAE and MSE play in regression.
How MAE Works
\[ MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i| \]where \(y_i\) is the actual value, \(\hat{y}_i\) the prediction, and \(n\) the number of data points. Taking absolute values removes the sign of each error without amplifying its size.
That linearity is what makes MAE robust: an error of 100 costs exactly ten times an error of 10, not a hundred times. The trade-off is at the training stage, where the absolute value has a kink at zero and a constant-magnitude gradient, which some optimizers handle less gracefully than MSE’s smooth curve.
MAE vs MSE
The practical difference: MAE weighs every unit of error equally, while MSE punishes large errors far more than small ones – so MAE is robust to outliers and MSE is sensitive to them. Choose MAE when a few extreme cases should not dominate the measure, and MSE when large errors are disproportionately costly.
| Criterion | MAE | MSE |
|---|---|---|
| Penalty on large errors | Proportional, so outliers count once | Squared, so outliers dominate the total |
| Units of the result | Same units as the target (e.g. dollars) | Squared units of the target (e.g. dollars²) |
| Gradient behavior | Constant magnitude, with a kink at zero | Grows with the error, smooth everywhere |
| Choose it when | Outliers should not dominate the score | Large errors are especially costly |
Example of MAE
A ride-hailing app predicts trip durations. Across 1,000 trips, its predictions miss the true duration by 3 minutes on average, so the MAE is 3 minutes, stated in the same units riders think in.
Now one trip hits an accident and runs 90 minutes over the prediction. Under MAE, that trip adds 90 error-minutes to the total, raising the average only slightly. Under MSE it would add 8,100 squared minutes and swamp the other 999 trips.
If the goal is a fair picture of everyday accuracy in time series forecasting like this, MAE gives it. The one freak trip stays one data point, not the whole story.
Related AI terms: MSE · Cross-Entropy Loss · Regression Analysis · Time Series · Model Evaluation
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Mihail Sebastian — Writes about AI governance, regulation, and the technology behind them. Placeholder bio — replace with a real credential line. About