mean absolute error
/ meen AB-suh-loot ER-ur /
Mean absolute error is the most down-to-earth way to score a number-predicting model: take how far off each prediction is, drop the minus signs, and average them. If your weather model is off by 2, 1, and 3 degrees on three days, its MAE is 2 degrees. It answers the plain question "on average, how many units am I wrong by?" — in the same units you started with.
Compared to mean squared error, MAE treats all mistakes proportionally: being off by 10 counts exactly ten times as much as being off by 1, no more. It does not square, so a single freak outlier can't blow up the score the way it does in MSE. This makes MAE robust — a trustworthy summary when your data has occasional wild values you don't want to dominate the verdict.
The trade-offs are real and worth knowing. Because MAE refuses to punish big errors extra-hard, it's the right choice when a 10-unit miss really is just ten 1-unit misses to you. But it's less smooth mathematically (it has a kink at zero), so it's a slightly fussier training target than MSE. And it's still not comparable across problems with different scales, so as with all error measures, judge it against a sensible baseline rather than in a vacuum.
Same four house-price errors as before: 2, 3, 1, 20. MAE = (2 + 3 + 1 + 20) / 4 = 6.5 (thousand dollars). The 20k miss matters, but it doesn't dwarf everything the way it did in MSE (103.5) — MAE keeps a steadier head when an outlier shows up.
Same data, gentler verdict: MAE doesn't let one outlier run away with the score.
Choosing between MAE and MSE is a value judgment, not a technicality: it encodes how much you dread large errors versus small ones. If one big miss truly is catastrophic (a bridge load, a dosage), MSE's harshness fits; if all errors are equally bad per unit, MAE is more faithful.