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Metric

MeanSquaredScaledError

API referenceSource
Multivariate

Mean squared scaled error (MSSE) or root mean squared scaled error (RMSSE).

Quickstart

python
from sktime.performance_metrics.forecasting import MeanSquaredScaledError

estimator = MeanSquaredScaledError(multioutput='uniform_average', multilevel='uniform_average', sp=1, square_root=False, by_index=False)

Parameters(5)

spint, default = 1
Seasonal periodicity of data.
square_rootbool, default = False
Whether to take the square root of the metric
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 MeanSquaredScaledError
>>> y_train = np. array ([5, 0.5, 4, 6, 3, 5, 2 ])
>>> y_true = np. array ([3, - 0.5, 2, 7, 2 ])
>>> y_pred = np. array ([2.5, 0.0, 2, 8, 1.25 ])
>>> rmsse = MeanSquaredScaledError (square_root = True)
>>> rmsse (y_true, y_pred, y_train = y_train) np.float64(0.20568833780186058)
>>> y_train = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_true = np. array ([[0.5, 1 ], [- 1, 1 ], [7, - 6 ]])
>>> y_pred = np. array ([[0, 2 ], [- 1, 2 ], [8, - 5 ]])
>>> rmsse (y_true, y_pred, y_train = y_train) np.float64(0.15679361328058636)
>>> rmsse = MeanSquaredScaledError (multioutput = 'raw_values', square_root = True)
>>> rmsse (y_true, y_pred, y_train = y_train) array([0.11215443, 0.20203051])
>>> rmsse = MeanSquaredScaledError (multioutput = [0.3, 0.7 ], square_root = True)
>>> rmsse (y_true, y_pred, y_train = y_train) np.float64(0.17451891814894502)

References

  1. M5 Competition Guidelines. https://mofc.unic.ac.cy/wp-content/uploads/2020/03/M5-Competitors-Guide-Final-10-March-2020.docx Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4.