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Metric

GeometricMeanSquaredError

API referenceSource
Multivariate

Geometric mean squared error (GMSE) or Root geometric mean squared error (RGMSE).

Quickstart

python
from sktime.performance_metrics.forecasting import GeometricMeanSquaredError

estimator = GeometricMeanSquaredError(multioutput='uniform_average', multilevel='uniform_average', square_root=False, by_index=False)

Parameters(4)

square_rootbool, default=False
Whether to take the square root of the mean squared error. If True, returns root geometric mean squared error (RGMSE) If False, returns geometric mean squared error (GMSE)
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 GeometricMeanSquaredError
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> gmse = GeometricMeanSquaredError ()
>>> gmse (y_true, y_pred) np.float64(2.80399089461488e-07)
>>> rgmse = GeometricMeanSquaredError (square_root = True)
>>> rgmse (y_true, y_pred) np.float64(0.000529527232030127)
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> gmse = GeometricMeanSquaredError ()
>>> gmse (y_true, y_pred) np.float64(0.5000000000115499)
>>> rgmse = GeometricMeanSquaredError (square_root = True)
>>> rgmse (y_true, y_pred) np.float64(0.5000024031086919)
>>> gmse = GeometricMeanSquaredError (multioutput = 'raw_values')
>>> gmse (y_true, y_pred) array([2.30997255e-11, 1.00000000e+00])
>>> rgmse = GeometricMeanSquaredError (multioutput = 'raw_values', square_root = True)
>>> rgmse (y_true, y_pred) array([4.80621738e-06, 1.00000000e+00])
>>> gmse = GeometricMeanSquaredError (multioutput = [0.3, 0.7 ])
>>> gmse (y_true, y_pred) np.float64(0.7000000000069299)
>>> rgmse = GeometricMeanSquaredError (multioutput = [0.3, 0.7 ], square_root = True)
>>> rgmse (y_true, y_pred) np.float64(0.7000014418652152)

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.