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Metric

MedianAbsolutePercentageError

API referenceSource
Multivariate

Median absolute percentage error (MdAPE) or symmetric version.

Quickstart

python
from sktime.performance_metrics.forecasting import MedianAbsolutePercentageError

estimator = MedianAbsolutePercentageError(multioutput='uniform_average', multilevel='uniform_average', symmetric=False, by_index=False, relative_to='y_true', eps=None)

Parameters(6)

symmetricbool, default = False
Whether to calculate the symmetric version of the percentage metric
relative_to{“y_true”, “y_pred”}, default=”y_true”

Determines the denominator of the percentage error.

  • If "y_true", the denominator is the true values,

  • If "y_pred", the denominator is the predicted values.

epsfloat, default=None
Numerical epsilon used in denominator to avoid division by zero. Absolute values smaller than eps are replaced by eps. If None, defaults to np.finfo(np.float64).eps
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 MedianAbsolutePercentageError
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> mdape = MedianAbsolutePercentageError (symmetric = False)
>>> mdape (y_true, y_pred) np.float64(0.16666666666666666)
>>> smdape = MedianAbsolutePercentageError (symmetric = True)
>>> smdape (y_true, y_pred) np.float64(0.18181818181818182)
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> mdape (y_true, y_pred) np.float64(0.5714285714285714)
>>> smdape (y_true, y_pred) np.float64(0.39999999999999997)
>>> mdape = MedianAbsolutePercentageError (multioutput = 'raw_values', symmetric = False)
>>> mdape (y_true, y_pred) array([0.14285714, 1. ])
>>> smdape = MedianAbsolutePercentageError (multioutput = 'raw_values', symmetric = True)
>>> smdape (y_true, y_pred) array([0.13333333, 0.66666667])
>>> mdape = MedianAbsolutePercentageError (multioutput = [0.3, 0.7 ], symmetric = False)
>>> mdape (y_true, y_pred) np.float64(0.7428571428571428)
>>> smdape = MedianAbsolutePercentageError (multioutput = [0.3, 0.7 ], symmetric = True)
>>> smdape (y_true, y_pred) np.float64(0.5066666666666666)

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.