Conformal splitconformal normalisedinterval

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SplitConformal.NormalisedInterval

The prediction interval whose width varies with the input: [ŷ − q·r̂, ŷ + q·r̂].

public static (double Lower, double Upper) NormalisedInterval(double prediction, double residualEstimate, double quantile)

Parameters — prediction is the model's point prediction for one new sample. residualEstimate is the second model's r̂ at that same sample, strictly positive. quantile is the calibrated quantile from Quantile over NormalisedResiduals.

Returns — a (double Lower, double Upper) tuple, in the target's own units.

Exceptions — ArgumentOutOfRangeException when quantile is negative or NaN, or when residualEstimate is zero, negative or NaN.

Example — one quantile, two points, two widths.

using Lodestar.Conformal;

double[] yTrue = [10.0, 12.0, 9.0, 15.0];
double[] yPredicted = [10.4, 11.0, 9.6, 13.5];
double[] residualEstimates = [0.5, 1.0, 0.5, 2.0];

double[] scores = SplitConformal.NormalisedResiduals(yTrue, yPredicted, residualEstimates);
double quantile = SplitConformal.Quantile(scores, alpha: 0.5);

(double Lower, double Upper) confident = SplitConformal.NormalisedInterval(11.0, 0.5, quantile);
(double Lower, double Upper) unsure = SplitConformal.NormalisedInterval(11.0, 2.0, quantile);

double tight = confident.Upper - confident.Lower;   // => 1
double wide = unsure.Upper - unsure.Lower;          // => 4

Returns, read — the same prediction and the same quantile, four times the width, because the second model says one point is four times as hard as the other. That is the whole difference from Interval, which would have given both the same.

Remarks — an infinite quantile yields the whole line, as Interval does: the multiplication carries the infinity through rather than turning it into NaN, which is what decision 0007 needs to hold here too.

Pass the estimate for the point being predicted, not the calibration mean. Passing a constant reduces this to Interval with the quantile rescaled, which is a valid thing to do and not what the score is for.

The guarantee assumes exchangeability — see the guide's Exchangeability section.

Applies to — net10.0, netstandard2.0.

See also — SplitConformal.NormalisedResiduals, SplitConformal.Interval.