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arxiv: 2605.16145 · v1 · pith:TUEKORGYnew · submitted 2026-05-15 · 📊 stat.ML · cs.LG

Skew-adaptive conformal prediction

Paulo C. Marques F. , Helton Graziadei This is my paper

Pith reviewed 2026-05-19 18:37 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords conformal predictionskew adaptationprediction intervalsregressionfinite-sample validityasymmetric intervalsgauge approach
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The pith

Skew-adaptive conformal prediction maintains finite-sample validity while adjusting interval shape to local skewness.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends split conformal prediction for regression by starting with an asymmetric interval family around a point prediction and deriving the corresponding conformity score via the gauge approach. An auxiliary predictive model is trained on the inverse hyperbolic sine transform of signed scaled residuals from the calibration set to learn how uncertainty should tilt across the feature space. This construction preserves the marginal coverage guarantee under exchangeability. On several datasets the resulting intervals show efficiency gains over both scaled-score conformal prediction and conformalized quantile regression. A separate calibration-based estimator is provided to anticipate the relative future width improvement.

Core claim

By training an auxiliary model to predict the inverse hyperbolic sine of signed scaled residuals, the procedure learns a feature-dependent skewness tilt that shapes asymmetric prediction intervals, while the overall split-conformal construction still guarantees the target marginal coverage probability under exchangeability.

What carries the argument

Conformity score induced by an asymmetric interval family through the gauge function, together with an auxiliary regressor trained on the asinh transform of signed scaled residuals to capture local skewness tilt.

Load-bearing premise

The additional predictive model trained on the inverse hyperbolic sine transform of signed scaled residuals can reliably capture the local skewness tilt across the feature space.

What would settle it

On a dataset exhibiting clear local skewness variation, the skew-adaptive intervals would fail to produce smaller average widths than scaled-score intervals while still meeting the nominal coverage level, or the calibration-based width-ratio estimator would deviate substantially from the observed test-set ratio.

Figures

Figures reproduced from arXiv: 2605.16145 by Helton Graziadei, Paulo C. Marques F..

Figure 1
Figure 1. Figure 1: Canonical and dual views of split conformal prediction. The canonical view starts from a specified conformity function. This function is evaluated on each calibra￾tion pair to produce conformity scores, and the resulting calibrated threshold defines the prediction interval as a sublevel set of the conformity function. The dual view starts from the opposite end: it first specifies a nondecreasing family of … view at source ↗
Figure 2
Figure 2. Figure 2: Prediction intervals for 30 test sample units from the Ames Housing, California Housing, and Bike Sharing datasets at nominal coverage level 1 − α = 0.90. For each test point, the figure displays the skew-adaptive conformal prediction interval in blue, the conformalized quantile regression interval in red, and the observed response, indicated by a black cross (×). The blue dot is the central prediction mad… view at source ↗
read the original abstract

We develop a skew-adaptive extension of split conformal prediction for regression. The method starts from an asymmetric interval family centered at a point prediction and uses the gauge approach to deduce the conformity score induced by this family. The inverse hyperbolic sine transform of signed scaled residuals provides the training target for an additional predictive model, whose role is to learn how predictive uncertainty should tilt across the feature space. The resulting procedure preserves the finite-sample marginal validity of split conformal prediction under exchangeability, while producing intervals that adapt to both local scale and local skewness. We also develop a calibration-sample-based estimator for comparing the expected relative future width of the skew-adaptive and classical scaled-score intervals. Experiments on a variety of datasets indicate gains in prediction interval efficiency over the scaled-score construction and conformalized quantile regression, and show that the proposed estimator closely matches the corresponding average width ratio observed on the test sample.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper proposes a skew-adaptive extension of split conformal prediction for regression. It constructs asymmetric prediction intervals centered at a point predictor, induces a conformity score via a gauge function on the asymmetric family, trains an auxiliary regressor on the inverse hyperbolic sine of signed scaled calibration residuals to predict local skewness tilt, and calibrates the quantile of the resulting scores. The central claim is that finite-sample marginal validity under exchangeability is preserved exactly as in standard split conformal prediction, while the intervals adapt to both local scale and local skewness; the paper also supplies a calibration-based estimator for the expected relative width versus the classical scaled-score method and reports efficiency gains on several datasets relative to scaled-score conformal prediction and conformalized quantile regression.

Significance. If the validity argument holds, the contribution is a practical, distribution-free method for incorporating skewness adaptation into conformal intervals without sacrificing the exact marginal coverage guarantee. The gauge-based construction and the auxiliary model on arcsinh-transformed residuals provide a clean separation between the validity mechanism (exchangeability of scores) and the efficiency mechanism (learned tilt), which is a useful conceptual advance. The proposed width-ratio estimator is a concrete tool for practitioners. Empirical results indicate consistent gains, though the magnitude depends on the auxiliary model's ability to capture skewness structure.

major comments (2)
  1. [§3.2] §3.2, gauge definition and score induction: the mapping from the asymmetric interval family to the conformity score must be shown to remain invariant under permutations of the calibration-plus-test points even after the auxiliary model's predicted tilt parameter is plugged in; a short explicit argument or lemma would strengthen the claim that exchangeability alone suffices for validity.
  2. [§5] §5, experimental comparison: the reported efficiency gains are measured against scaled-score conformal prediction and CQR, but the paper does not report the auxiliary model's out-of-sample R² or calibration error on the arcsinh targets; without this diagnostic it is difficult to attribute the width reductions specifically to successful skewness adaptation versus other factors.
minor comments (3)
  1. [§3] Notation for the auxiliary model's output (predicted skewness parameter) should be introduced once and used consistently; currently the symbol appears to vary between the method section and the experiments.
  2. [§5] Figure 2 (or equivalent width-ratio plot): axis labels and legend entries should explicitly state whether the plotted ratio is the estimator or the realized test-set ratio.
  3. [Abstract] The abstract and §1 claim 'gains in prediction interval efficiency'; a brief statement of the average width reduction (with standard error) across datasets would make this quantitative claim easier to evaluate at a glance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the constructive suggestions. We address the two major comments below and will incorporate clarifications and additional diagnostics in the revised manuscript.

read point-by-point responses

  1. Referee: [§3.2] §3.2, gauge definition and score induction: the mapping from the asymmetric interval family to the conformity score must be shown to remain invariant under permutations of the calibration-plus-test points even after the auxiliary model's predicted tilt parameter is plugged in; a short explicit argument or lemma would strengthen the claim that exchangeability alone suffices for validity.

    Authors: We agree that an explicit argument strengthens the presentation. The auxiliary regressor is trained exclusively on the calibration residuals and then applied uniformly as a fixed function to compute the gauge-based conformity score for every point in the calibration-plus-test collection. Because the underlying data points remain exchangeable and the score mapping (once the tilt predictor is fixed) is the same deterministic function for all points, the resulting scores are exchangeable. In the revision we will insert a short lemma in §3.2 that makes this invariance explicit, following the standard split-conformal argument. revision: yes

  2. Referee: [§5] §5, experimental comparison: the reported efficiency gains are measured against scaled-score conformal prediction and CQR, but the paper does not report the auxiliary model's out-of-sample R² or calibration error on the arcsinh targets; without this diagnostic it is difficult to attribute the width reductions specifically to successful skewness adaptation versus other factors.

    Authors: We acknowledge that reporting the auxiliary model's fit quality would help readers attribute the observed width reductions. Because the auxiliary model is trained on the calibration set, a strictly out-of-sample evaluation would require a further data split, which we did not perform in the original experiments. In the revision we will add the in-sample R² and mean absolute calibration error of the auxiliary regressor on the arcsinh targets for each dataset, together with a brief discussion of how these diagnostics relate to the reported efficiency gains. We view this as a partial revision because a true held-out evaluation would alter the experimental protocol. revision: partial

Circularity Check

0 steps flagged

Validity from exchangeability; adaptation learned from residuals without circularity

full rationale

The derivation chain begins with the standard split conformal prediction construction under exchangeability and defines an asymmetric interval family whose induced conformity score preserves the uniform rank property of the test point. The auxiliary model is trained on arcsinh-transformed signed scaled residuals from the calibration set to predict local tilt; this step is an efficiency modification whose output does not enter the validity argument. No equation reduces the coverage guarantee to a fitted parameter or to a self-citation chain. The paper remains self-contained against the external benchmark of exchangeability-based marginal coverage.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the exchangeability assumption standard to conformal prediction plus the effectiveness of the auxiliary model in capturing skewness; no new free parameters beyond those of the auxiliary model are introduced at the abstract level.

free parameters (1)
  • parameters of the auxiliary skewness model
    An additional predictive model is trained on transformed residuals, introducing fitted parameters that determine the local tilt.
axioms (1)
  • domain assumption The data points are exchangeable.
    Invoked to guarantee finite-sample marginal validity of the conformal procedure.

pith-pipeline@v0.9.0 · 5672 in / 1359 out tokens · 64942 ms · 2026-05-19T18:37:30.489429+00:00 · methodology

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