mae – Mean absolute error – (1/N) Σ |y_t - ŷ_t|.#

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Operational op under axis point_metrics, sub-layer L5_A_metric_specification, layer l5. Standalone callable: mf.functions.mae.

Function signature#

mf.functions.mae(
    y_true: np.ndarray | pd.Series,
    y_pred: np.ndarray | pd.Series,
) -> float

Parameters#

name

type

default

constraint

description

y_true

`np.ndarray

pd.Series`

—

—

y_pred

`np.ndarray

pd.Series`

—

—

Returns#

float — scalar result.

Behavior#

Point-forecast metric mae. L1 loss; robust alternative to MSE. Equally weighs every absolute residual rather than penalising large errors super-linearly. The implicit decision rule under MAE is the median of the predictive distribution (vs the mean for MSE).

When to use

Heavy-tailed targets where extreme errors should not dominate; reporting in target units.

When NOT to use

When the squared-loss decision rule is what the user actually faces.

In recipe context#

Set params.point_metrics = "mae" in the relevant layer to activate this op within a recipe:

# Layer L5 recipe fragment
params:
  point_metrics: mae

References#

  • macroforecast design Part 3, L5: ‘evaluation = (metric × benchmark × aggregation × decomposition × ranking).’

  • Diebold (2017) ‘Forecasting in Economics, Business, Finance and Beyond’, University of Pennsylvania (free online). https://www.sas.upenn.edu/~fdiebold/Textbooks.html