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Metric

MeanLinexError

API referenceSource
Multivariate

Mean Linear Exponential (LinEx) error.

Quickstart

python
from sktime.performance_metrics.forecasting import MeanLinexError

estimator = MeanLinexError(a=1.0, b=1.0, multioutput='uniform_average', multilevel='uniform_average', by_index=False)

Parameters(5)

aint or float, default = 1

Controls whether over- or under- predictions receive an approximately linear or exponential penalty. If a > 0 then negative errors (over-predictions) are penalized approximately linearly and positive errors (under-predictions) are penalized approximately exponentially. If a < 0 the reverse is true.

bint or float, default = 1
Multiplicative penalty to apply to calculated errors controlled by scale parameter.
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 MeanLinexError
>>> linex_error = MeanLinexError ()
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> linex_error (y_true, y_pred) np.float64(0.19802627763937575)
>>> linex_error = MeanLinexError (b = 2)
>>> linex_error (y_true, y_pred) np.float64(0.3960525552787515)
>>> linex_error = MeanLinexError (a =- 1)
>>> linex_error (y_true, y_pred) np.float64(0.2391800623225643)
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> linex_error = MeanLinexError ()
>>> linex_error (y_true, y_pred) np.float64(0.2700398392309829)
>>> linex_error = MeanLinexError (a =- 1)
>>> linex_error (y_true, y_pred) np.float64(0.49660966225813563
>>> linex_error = MeanLinexError (multioutput = 'raw_values')
>>> linex_error (y_true, y_pred) array([0.17220024, 0.36787944])
>>> linex_error = MeanLinexError (multioutput = [0.3, 0.7 ])
>>> linex_error (y_true, y_pred) np.float64(0.30917568000716666)

References

  1. [1 ] Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4. [2 ] Diebold, Francis X. (2007). “Elements of Forecasting (4th ed.)”, Thomson, South-Western: Ohio, US.