skfolio.metrics.mahalanobis_calibration_loss#

skfolio.metrics.mahalanobis_calibration_loss(estimator, X_test, y=None)[source]#

Mahalanobis calibration loss.

Computes the absolute deviation of mahalanobis_calibration_ratio from its calibration target of 1.0.

Let \(r_t\) be the one-period realized return vector at time \(t\), and let \(R^{(h)} = \sum_{t=1}^{h} r_t\) be the aggregated return over an evaluation window of \(h\) observations.

\[\ell = \left\lvert \frac{{R^{(h)}}^\top (h\,\Sigma)^{-1} R^{(h)}}{n} - 1 \right\rvert\]

where \(n\) is the number of assets.

As with mahalanobis_calibration_ratio, heavy tails and regime changes can weaken the Gaussian reference. This loss is therefore often most useful for relative comparison across covariance estimators.

Parameters:

estimatorBaseEstimator: Fitted estimator, must expose covariance_ or return_distribution_.covariance.
X_testarray-like of shape (n_observations, n_assets): Realized returns for the test window.
yIgnored: Present for scikit-learn API compatibility.

Returns:

float: Calibration loss. Lower values are better and the optimum is 0.0.