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Metric

GeometricMeanSquaredError

API-ReferenzQuellcode
Multivariate

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

If square_root is False then calculates GMSE and if square_root is True then RGMSE is calculated. Both GMSE and RGMSE return non-negative floating point. The best value is approximately zero, rather than zero.

Like MSE and MdSE, GMSE is measured in squared units of the input data. RMdSE is on the same scale as the input data like RMSE and RdMSE. Because GMSE and RGMSE square the forecast error rather than taking the absolute value, they penalize large errors more than GMAE.

Schnellstart

python
from sktime.performance_metrics.forecasting import GeometricMeanSquaredError

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

Parameter(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.

Beispiele

>>> 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)

Referenzen

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