Median absolute error

• Es robusto a outliers.

• Se computa como:

  \text{MedAE}(y_i, \hat{y}_i) = \text{median}(|y_1 - \hat{y}_1|, \dots, |y_n - \hat{y}_n| = \text{median}(|\hat{e}_1|, \dots, |\hat{e}_n|)

from sklearn.metrics import median_absolute_error

y_true = [3.0, -0.5, 2, 7]
y_pred = [2.5, +0.0, 2, 8]

# median(0.5, 0.5, 0.0, 1.0) = 0.5

median_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]]

# median(0.5, 0.0, 1.0) = 0.5
# median(1.0, 1.0, 1.0) = 1.0
median_absolute_error(
    y_true,
    y_pred,
    multioutput="raw_values",
)

array([0.5, 1. ])

#
# 0.5 * (0.5 + 1.0) = 0.75
#
median_absolute_error(
    y_true,
    y_pred,
)

0.75

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

0.85