SquaredDistrLoss

class SquaredDistrLoss(multioutput='uniform_average', multivariate=False)[source]

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.

Parameters:

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

Methods

__call__(y_true, y_pred, **kwargs)

Calculate metric value using underlying metric function.

__call__(y_true, y_pred, **kwargs)[source]

Calculate metric value using underlying metric function.

Parameters:

y_truepd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon: Ground truth (correct) target values.
y_predreturn object of probabilistic prediction method scitype:y_pred: must be at fh and for variables equal to those in y_true.

Returns:

lossfloat or 1-column pd.DataFrame with calculated metric value(s)

metric is always averaged (arithmetic) over fh values if multioutput = “raw_values”,

will have a column level corresponding to variables in y_true

if multioutput = multioutput = “uniform_average” or or array-like: entries will be averaged over output variable column
if score_average = False,: will have column levels corresponding to quantiles/intervals
if score_average = True,: entries will be averaged over quantiles/interval column