Mean absolute error (MAE)

• Es una métrica de riesgo equivalente al valor esperado del error absoluto o norma L1.

• Esta métrica no es sensitiva hacia los outliers.

• Una desventaja de su uso como métrica en optimización es que el gradiente depende del signo del error y no de su magnitud.

• Se computa como:

  \text{MAE}(y, \hat{y}) = \frac{1}{n_{\text{samples}}} \sum_{i=0}^{n_{\text{samples}} - 1} |y_i - \hat{y}_i| = \frac{1}{n_{\text{samples}}} \sum_{i=0}^{n_{\text{samples}} - 1} |\hat{e}_i|

from sklearn.metrics import mean_absolute_error

y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]

mean_absolute_error(
    # -------------------------------------------------------------------------
    # Ground truth (correct) target values.
    y_true=y_true,
    # -------------------------------------------------------------------------
    # Estimated target values.
    y_pred=y_pred,
    # -------------------------------------------------------------------------
    # Sample weights.
    sample_weight=None,
    # -------------------------------------------------------------------------
    # Defines aggregating of multiple output scores.
    # * 'raw_values': Returns a full set of scores in case of multioutput input.
    # * 'uniform_average': Scores of all outputs are averaged with uniform
    #      weight.
    multioutput="uniform_average",
)

0.5

y_true = [[0.5, 1], [-1, 1], [7, -6]]
y_pred = [[0.0, 2], [-1, 2], [8, -5]]

mean_absolute_error(
    y_true,
    y_pred,
    multioutput="raw_values",
)

array([0.5, 1. ])

mean_absolute_error(
    y_true,
    y_pred,
)

0.75

#
# 0.5 * 0.3 + 1.0 * 0.7 = 0.85
#
mean_absolute_error(
    y_true,
    y_pred,
    multioutput=[0.3, 0.7],
)

0.85