Metric

MedianAbsoluteError

Median absolute error (MdAE).

MdAE output is non-negative floating point. The best value is 0.0.

Like MAE, MdAE is on the same scale as the data. Because MAE takes the absolute value of the forecast error rather than squaring it, MAE penalizes large errors to a lesser degree than MdSE or RdMSE.

Taking the median instead of the mean of the absolute errors also makes this metric more robust to error outliers since the median tends to be a more robust measure of central tendency in the presence of outliers.

For a univariate, non-hierarchical sample of true values \(y_1, \dots, y_n\) and predicted values \(\widehat{y}_1, \dots, \widehat{y}_n\), at time indices \(t_1, \dots, t_n\), evaluate or call returns the Median Absolute Error, \(\text{median}\left(|y_i - \widehat{y}_i|\right)_{i=1}^{n}\).

multioutput and multilevel control averaging across variables and hierarchy indices, see below.

evaluate_by_index returns, at a time index \(t_i\), the absolute error at that time index, \(|y_i - \widehat{y}_i|\), for all time indices \(t_1, \dots, t_n\) in the input.

Schnellstart

python

from sktime.performance_metrics.forecasting import MedianAbsoluteError

estimator = MedianAbsoluteError(multioutput='uniform_average', multilevel='uniform_average', by_index=False)

Parameter(3)

multioutput‘uniform_average’ (default), 1D array-like, or ‘raw_values’: Whether and how to aggregate metric for multivariate (multioutput) data.
If 'uniform_average' (default), errors of all outputs are averaged with uniform weight.
If 1D array-like, errors are averaged across variables, with values used as averaging weights (same order).
If 'raw_values', does not average across variables (outputs), per-variable errors are returned.
multilevel{‘raw_values’, ‘uniform_average’, ‘uniform_average_time’}: How to aggregate the metric for hierarchical data (with levels).
If 'uniform_average' (default), errors are mean-averaged across levels.
If 'uniform_average_time', metric is applied to all data, ignoring level index.
If 'raw_values', does not average errors across levels, hierarchy is retained.
by_indexbool, default=False: Controls averaging over time points in direct call to metric object.
If False (default), direct call to the metric object averages over time points, equivalent to a call of the evaluate method.
If True, direct call to the metric object evaluates the metric at each time point, equivalent to a call of the evaluate_by_index method.

Beispiele

>>> import numpy as np
>>> from sktime.performance_metrics.forecasting import MedianAbsoluteError
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> mdae = MedianAbsoluteError ()
>>> mdae (y_true, y_pred) np.float64(0.5)
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> mdae (y_true, y_pred) np.float64(0.75)
>>> mdae = MedianAbsoluteError (multioutput = 'raw_values')
>>> mdae (y_true, y_pred) array([0.5, 1. ])
>>> mdae = MedianAbsoluteError (multioutput = [0.3, 0.7 ])
>>> mdae (y_true, y_pred) np.float64(0.85)

Referenzen

Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4.