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The prediction interval at one test point for the gamma score, conformity_score="gamma" of MAPIE's cross-conformal regressors.

public static (double Lower, double Upper) GammaInterval(ReadOnlySpan<double> testPredictions, ReadOnlySpan<bool> heldOut, ReadOnlySpan<double> scores, double alpha, CrossConformalMethod method = CrossConformalMethod.Plus, CrossConformalAggregation aggregation = CrossConformalAggregation.Mean)

public static (double Lower, double Upper) GammaInterval(ReadOnlySpan<double> testPredictions, ReadOnlySpan<int> folds, ReadOnlySpan<double> scores, double alpha, CrossConformalMethod method = CrossConformalMethod.Plus)

Parameters — testPredictions is each model's prediction at the test point, and every held-out one must be strictly positive. heldOut is the n × M mask, or folds one model index per training sample. scores come from SplitConformal.GammaScores. alpha is the miscoverage level; method and aggregation are as for CrossConformal.Interval.

Returns — the interval's two bounds, either of them infinite when there are too few samples for its side's level.

Exceptions — ArgumentOutOfRangeException when alpha is not strictly between 0 and 1, when a fold is outside [0, M), when an enum value is not declared, or when a held-out prediction at the test point is not strictly positive; ArgumentException as for Interval.

Example — relative errors, so the interval widens with the prediction.

using Lodestar.Conformal;

// Six training samples in three folds; model m was fitted without fold m.
int[] folds = [0, 0, 1, 1, 2, 2];
double[] yTrue = [10.2, 11.5, 9.8, 12.6, 11.1, 10.4];
double[] outOfFold = [10.7, 10.5, 10.0, 11.8, 11.4, 11.0];   // each sample's prediction by its fold's model
double[] atTest = [10.0, 11.0, 12.0];                        // the three models' predictions at a new point

double[] scores = SplitConformal.GammaScores(yTrue, outOfFold);
(double lower, double upper) = CrossConformal.GammaInterval(atTest, folds, scores, 0.3);

double low = lower;     // => 9.532710280373832
double high = upper;    // => 11.745762711864405

Remarks — plus reads ŷ₋ᵢ(x)(1 + Rᵢ) over the training samples, min-max widens the smallest and largest held-out prediction by 1 + q. The score is not symmetric, so each side reads its own quantile at α/2, as MAPIE's does; the lower side's level is evaluated as MAPIE evaluates it, (1 − 2a) + a, which moves the rank by one at some sizes.

Applies to — net10.0, netstandard2.0.

See also — SplitConformal.GammaInterval, CrossConformal.Interval.