Mean Absolute Error (MAE)

Mean Absolute Error (MAE) is the arithmetic mean of the absolute differences between estimated values and reference (ground-truth) values across a set of observations. For a calorie-estimation method evaluated against laboratory-weighed reference meals, MAE is expressed in kilocalories: the average by which the method's estimate deviates from the measured truth, ignoring direction. It is the most interpretable first-line accuracy measure in dietary-assessment methodology precisely because its units match the units of the quantity being measured.

The formula

For n observations, each with an estimated value ê_i and a reference value e_i:

MAE = (1/n) × Σ |ê_i − e_i|

That is all. The absolute-value operator is the critical detail: it prevents signed errors from cancelling. A method that over-estimates by 100 kcal on half its observations and under-estimates by 100 kcal on the other half has a signed mean error near zero — which would flatter the method if reported alone — but an MAE of roughly 100 kcal, which accurately reflects that the method is never particularly close.

Why MAE and not signed bias

A dietary-assessment method's signed bias — the mean of (estimate − reference) — is a distinct and useful statistic that captures whether the method systematically over- or under-estimates. It should be reported alongside MAE, not instead of it. A method with MAE 120 kcal and signed bias near zero is noisy but unbiased; a method with MAE 120 kcal and signed bias +100 kcal is almost entirely systematic over-estimation. The distinction matters for deciding whether a recalibration constant could improve the method.

MAE vs RMSE

The choice between MAE and Root Mean Square Error is partly technical and partly aesthetic. RMSE punishes large errors more severely because it squares them before averaging; MAE weights all errors linearly. A method that is 50 kcal off on 99 meals and 500 kcal off on one meal will have an MAE near 55 kcal and an RMSE closer to 80 kcal. Researchers favour RMSE when the downstream cost of large errors is disproportionately bad (for example, insulin-dose estimation in type 1 diabetes); MAE when the downstream cost is roughly linear in error magnitude (typical calorie-tracking use cases).

What a meaningful MAE report looks like

Any published MAE figure is meaningless without four pieces of context:

• The reference set it was measured against (a specific laboratory-weighed meal set, with an n).
• The year of measurement (because food databases and app models drift).
• The statistical method used (mean MAE across meals, or weighted, or median as a robust alternative).
• The signed bias reported alongside.

A claim of "accurate to within 50 kcal" without these qualifiers is marketing, not methodology. A claim of "MAE 48.7 kcal against the Bitebench 2026 reference set (n=500 meals), signed bias −12 kcal" is a methodological statement and can be reproduced or challenged.