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arxiv: 2605.07963 · v1 · submitted 2026-05-08 · 💻 cs.LG

Recognition: no theorem link

Aggregation in conformal e-classification

Vladimir Vovk
Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:27 UTC · model grok-4.3

classification 💻 cs.LG
keywords conformal predictione-predictorsaggregationcross-conformalmachine learningvalidityclassificationexperimental evaluation
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The pith

Conformal e-predictors can be aggregated more flexibly than standard conformal predictors while retaining validity.

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

This paper focuses on combining multiple conformal e-predictors into a single system. Conformal e-predictors have the property that their aggregation preserves validity guarantees more readily than other conformal approaches. The work runs experiments on the established cross-conformal e-prediction technique and on new variants designed to be simpler in concept and broader in use. Readers care because aggregation lets practitioners trade off prediction accuracy against computation time without invalidating the underlying guarantees.

Core claim

An important advantage of conformal e-predictors is that they are easier to aggregate without sacrificing their validity. The paper studies experimentally cross-conformal e-prediction, which is an existing method of aggregating conformal e-predictors, and its modifications that are conceptually simpler and more flexible.

What carries the argument

Cross-conformal e-prediction, the method that merges e-predictors trained on different data splits or folds to form a combined predictor.

If this is right

  • Practitioners can combine several e-predictors to reach better efficiency without extra validity cost.
  • The simpler modifications allow aggregation in settings where the original cross-conformal procedure is inconvenient to implement.
  • Predictive performance and computational load can be balanced more directly in e-classification tasks.
  • Validity remains approximately intact after aggregation, supporting reliable use in applications that require guarantees.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The flexibility of these methods could support incremental updating of predictors as new data arrives without full retraining.
  • Similar aggregation ideas might apply to regression or other output types beyond classification.
  • If the simpler variants scale to very large datasets, they could reduce the engineering effort needed for valid predictive systems.

Load-bearing premise

The observed behavior of the aggregation methods on the chosen datasets and tasks will continue to hold on new data and different classification problems.

What would settle it

Apply the same aggregation procedures to several fresh, unrelated classification datasets and measure whether the combined e-predictors violate their validity bounds substantially more often than the individual predictors do.

Figures

Figures reproduced from arXiv: 2605.07963 by Vladimir Vovk.

Figure 1
Figure 1. Figure 1: Results for CEP with different degrees of ordinariness [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Results for ICP; l = 12,000, Y = 2 (left), Y = 10 (top), and Y = 100 (right). The average value of the AFS criterion over 10,000 iterations is shown as function of the size m = 1, . . . , l − 1 of the proper training set. This is for Jeffreys’s prior, α = 0.5. percentage of calibration observations is small, whereas for Y = 2 it is very close to 1; the situation for Y = 10 is intermediate. This is natural … view at source ↗
Figure 3
Figure 3. Figure 3: Results for ICEP, averaged over 10,000 iterations; [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Results for CCP; l = 12,000, Y = 10 (left), Y = 100 (right), and α = 0.5. The value of the AFS criterion is averaged over 10,000 iterations and shown as function of the number of folds. Proposition 5. On the same data, a leave-one-out CCP produces the same p-values as the corresponding full conformal p-predictor. 6.2 CCEP For cross-conformal e-prediction (CCEP), we compute the e-value (23) for each fold k … view at source ↗
Figure 5
Figure 5. Figure 5: Results for CCEP; l = 12,000, Y = 10 (left), Y = 100 (right), and α = 0.5. The average value of the AFES criterion over 10,000 iterations is shown as function of the number of folds (smallest divisors of l). to some degree, by RICEP, which will be introduced in the next section. 7 RICEP and BICEP It is clear that CCEP, even if complemented by inverse CCEP, is too inflexible since the number K of folds can … view at source ↗
Figure 6
Figure 6. Figure 6: Results for the inverse CCEP: the full picture is in the left panel [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Results for CCEP vs RICEP; l = 12,000, Y = 10, and α = 0.5. The average value of the AFES criterion over 10,000 iterations is shown as function of the number of folds (the 7 smallest divisors of l). efficiency that involves logarithms (see (2)). In principle, it does not mean that an improvement from, say, RICEP 1 to RICEP 100 in [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The analogue of Figure 7 for [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The analogue of Figure 7 for [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: A histogram of RICEP e-values, as described in text. [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
read the original abstract

Aggregating conformal predictors is a standard way of balancing their predictive and computational efficiency while retaining their validity, at least approximately. An important advantage of conformal e-predictors is that they are easier to aggregate without sacrificing their validity. This paper studies experimentally cross-conformal e-prediction, which is an existing method of aggregating conformal e-predictors, and its modifications that are conceptually simpler and more flexible.

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

0 major / 1 minor

Summary. The manuscript experimentally studies cross-conformal e-prediction, an existing method for aggregating conformal e-predictors, along with conceptually simpler and more flexible modifications. It frames the ease of aggregation for e-predictors (without sacrificing validity) as background motivation for the experimental comparison.

Significance. If the experimental comparisons hold, the work could provide practical guidance on simpler aggregation strategies for conformal predictors, which is relevant for balancing validity guarantees with computational efficiency in machine learning applications. The experimental framing allows direct assessment of the proposed modifications relative to the existing cross-conformal approach.

minor comments (1)
  1. [Abstract] The abstract describes an experimental study but provides no details on datasets, baselines, error bars, or statistical tests, making it impossible to assess whether the data supports the claims about simplicity and flexibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive review and recommendation of minor revision. We appreciate the acknowledgment that the experimental comparisons could offer practical guidance on aggregation strategies for conformal e-predictors.

Circularity Check

0 steps flagged

No significant circularity; experimental evaluation of existing methods

full rationale

The paper is framed as an experimental study of cross-conformal e-prediction (an existing method) and its modifications for aggregating conformal e-predictors. No derivations, equations, fitted parameters presented as predictions, or load-bearing self-citations are indicated in the provided abstract or description. The stated advantage of e-predictors for aggregation is background context rather than a new claim derived within the paper. The work is self-contained as empirical evaluation without reducing any central result to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical derivations, free parameters, axioms, or invented entities are described in the abstract; the work is purely experimental.

pith-pipeline@v0.9.0 · 5339 in / 1018 out tokens · 26857 ms · 2026-05-11T02:27:10.064970+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

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    arXiv preprint arXiv:2411.11824 , year=

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    Vladimir Vovk, Alexander Gammerman, and Glenn Shafer.Algorithmic Learn- ing in a Random World

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    work page arXiv 1912

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    (2022, Sect

    21 A Some proofs A.1 Proof of Proposition 1 The argument of Vovk et al. (2022, Sect. 3.4.1, Remark 3.15) can be modified to cover this case as well (it is not covered by the original argument since the functionp∈[0,1]→ −lnptakes value∞atp:= 0, as mentioned at the end of the remark). Namely, we can replace the second displayed equation in Vovk et al. (2022...

    work page 2022

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    Then (11) holds conditionally on the training set and, therefore, unconditionally

    conditionally on the training set. Then (11) holds conditionally on the training set and, therefore, unconditionally. To show that there is a unique solution to (11), suppose there are two dif- ferent solutions. Then their arithmetic mean will provide a better value for the objective function in (11) by Jensen’s inequality. The value will be strictly bet-...

    work page 2025