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Metric

MeanRelativeAbsoluteError

API referenceSource
Multivariate

Mean relative absolute error (MRAE).

Quickstart

python
from sktime.performance_metrics.forecasting import MeanRelativeAbsoluteError

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

Parameters(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.

Examples

>>> import numpy as np
>>> from sktime.performance_metrics.forecasting import MeanRelativeAbsoluteError
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> y_pred_benchmark = y_pred * 1.1
>>> mrae = MeanRelativeAbsoluteError ()
>>> mrae (y_true, y_pred, y_pred_benchmark = y_pred_benchmark) np.float64(0.9511111111111111)
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> y_pred_benchmark = y_pred * 1.1
>>> mrae (y_true, y_pred, y_pred_benchmark = y_pred_benchmark) np.float64(0.8703703703703702)
>>> mrae = MeanRelativeAbsoluteError (multioutput = 'raw_values')
>>> mrae (y_true, y_pred, y_pred_benchmark = y_pred_benchmark) array([0.51851852, 1.22222222])
>>> mrae = MeanRelativeAbsoluteError (multioutput = [0.3, 0.7 ])
>>> mrae (y_true, y_pred, y_pred_benchmark = y_pred_benchmark) np.float64(1.0111111111111108)

References

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