mean_relative_absolute_error#

mean_relative_absolute_error(y_true, y_pred, horizon_weight=None, multioutput='uniform_average', **kwargs)[source]#

Mean relative absolute error (MRAE).

In relative error metrics, relative errors are first calculated by scaling (dividing) the individual forecast errors by the error calculated using a benchmark method at the same index position. If the error of the benchmark method is zero then a large value is returned.

MRAE applies mean absolute error (MAE) to the resulting relative errors.

Parameters:
y_truepd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Ground truth (correct) target values.

y_predpd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Forecasted values.

horizon_weightarray-like of shape (fh,), default=None

Forecast horizon weights.

multioutput{‘raw_values’, ‘uniform_average’} or array-like of shape (n_outputs,), default=’uniform_average’

Defines how to aggregate metric for multivariate (multioutput) data. If array-like, values used as weights to average the errors. If ‘raw_values’, returns a full set of errors in case of multioutput input. If ‘uniform_average’, errors of all outputs are averaged with uniform weight.

y_pred_benchmarkpd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon, default=None

Forecasted values from benchmark method. Passed by kwargs.

Returns:
lossfloat

MRAE loss. If multioutput is ‘raw_values’, then MRAE is returned for each output separately. If multioutput is ‘uniform_average’ or an ndarray of weights, then the weighted average MRAE of all output errors is returned.

References

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

Examples

>>> from aeon.performance_metrics.forecasting import mean_relative_absolute_error
>>> 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
>>> mean_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark)
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
>>> mean_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark)
0.8703703703703702
>>> mean_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark, multioutput='raw_values')
array([0.51851852, 1.22222222])
>>> mean_relative_absolute_error(y_true, y_pred,     y_pred_benchmark=y_pred_benchmark, multioutput=[0.3, 0.7])
1.0111111111111108