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Metric

SquaredDistrLoss

API referenceSource
Multivariate

Squared loss for distributional predictions.

Also known as:

  • continuous Brier loss

  • Gneiting loss

  • (mean) squared error/loss, i.e., confusingly named the same as the point prediction loss commonly known as the mean squared error

For a predictive distribution \(d\) and a ground truth value \(y\), the squared (distribution) loss is defined as \(L(y, d):= -2 p_d(y) + \|p_d\|^2\), where \(\|p_d\|^2\) is the (function) L2-norm of \(p_d\).

  • evaluate computes the average test sample loss.

  • evaluate_by_index produces the loss sample by test data point.

  • multivariate controls averaging over variables.

Quickstart

python
from sktime.performance_metrics.forecasting.probabilistic import SquaredDistrLoss

estimator = SquaredDistrLoss(multioutput='uniform_average', multivariate=False)

Parameters(2)

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.

multivariatebool, optional, default=False

  • if True, behaves as multivariate squared loss: the score is computed for entire row, results one score per row

  • if False, is univariate squared loss: the score is computed per variable marginal, results in many scores per row