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CrossConformal

Cross-conformal regression: CV+, Jackknife+ and the jackknife-after-bootstrap, at MAPIE parity, with no calibration set held out.

public static class CrossConformal

Example — CV+ over three folds, at 70 % coverage.

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.AbsoluteResiduals(yTrue, outOfFold);
(double lower, double upper) = CrossConformal.Interval(atTest, folds, scores, alpha: 0.3);

double low = lower;     // => 9.5
double high = upper;    // => 12.3

Remarks — SplitConformal spends a calibration set the model never sees. This class spends nothing: every training sample is scored by a model fitted without it, and a new point's interval is built from every model's prediction there. Model m of M is fitted without the samples its column of a held-out mask marks — one fold each for CV+, one sample each for Jackknife+, a bootstrap's out-of-bag samples for the jackknife-after-bootstrap. As everywhere in this package the models are yours: this takes their predictions.

The guarantee is 1 − 2α for CV+ and Jackknife+ (Barber et al., 2021), not the 1 − α of split conformal, though coverage near 1 − α is what is usually observed. It assumes exchangeability — see the guide's Exchangeability section.

MAPIE's method="base" is the split interval over the out-of-sample scores: SplitConformal.Interval around the model fitted on every sample, at SplitConformal.Quantile of the scores, or SplitConformal.GammaInterval for the gamma score.

Applies to — net10.0, netstandard2.0.

See also — the conformal index, SplitConformal.

Members

Member	What it does
CrossConformal.OutOfSample	Each training sample's prediction by the models fitted without it.
CrossConformal.Interval	The interval at a test point for the absolute-residual score.
CrossConformal.GammaInterval	The interval at a test point for the gamma score.
CrossConformalMethod	Plus or min-max.
CrossConformalAggregation	Mean or median, over the models that held a sample out.