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A predictor abstains when its expected regret to the full-knowledge Bayes model exceeds a rejection cost, marking inputs where training data is insufficient.

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Introduces a Bayesian framework for reject-option prediction that abstains based on expected regret from epistemic uncertainty when training data is limited.

T0 review reviewed 2026-05-18 challenge →

load-bearing objection The paper frames epistemic rejection as regret minimization against the unknown Bayes-optimal predictor, but leaves the practical estimation of that regret from finite data unclear. the 2 major comments →

arxiv 2511.04855 v2 submitted 2025-11-06 cs.AI

Epistemic Reject Option Prediction

Vojtech Franc , Jakub Paplham This is my paper
classification cs.AI
keywords epistemic uncertaintyreject optionBayesian learningregret minimizationabstentionuncertainty quantificationlimited dataprediction with rejection
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper introduces an epistemic reject-option predictor that abstains on inputs where the expected performance gap to the ideal Bayes-optimal predictor is larger than a given cost. Traditional reject methods handle only uncertainty from random noise under the assumption of plentiful data, but this approach explicitly targets uncertainty from limited training data by redefining optimality through Bayesian regret minimization. The model decides to reject rather than predict when the regret for that input crosses the rejection threshold. A sympathetic reader would care because many practical deployments involve sparse data, where guessing on poorly supported inputs can lead to costly errors in high-stakes settings. If the framework is correct, it supplies a direct way to detect and avoid reliance on predictions that lack adequate data support.

Core claim

The optimal epistemic reject-option predictor abstains for a given input when the conditional expected regret exceeds the rejection cost, where regret measures the gap in expected loss between the learned predictor and the Bayes-optimal predictor that knows the true data distribution. This definition follows from minimizing the Bayesian expected loss that incorporates the option to abstain and pay the fixed rejection cost instead of predicting.

What carries the argument

Expected regret to the Bayes-optimal predictor, which quantifies the performance gap caused by limited data and triggers abstention when it exceeds the rejection cost.

Load-bearing premise

The expected regret relative to the Bayes-optimal predictor can be meaningfully estimated or bounded from the learned model despite having only limited data.

What would settle it

An experiment on data with a known true distribution showing that the model's abstention regions fail to match the inputs where its actual performance gap to the Bayes-optimal predictor is largest would disprove the central claim.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper introduces an epistemic reject-option predictor that abstains on inputs where expected regret relative to the Bayes-optimal predictor (with full knowledge of the data distribution) exceeds a rejection cost. Building on Bayesian learning, it redefines optimality in terms of this regret to address epistemic uncertainty in limited-data regimes, claiming to be the first principled framework for identifying inputs unsupported by available training data.

Significance. If the central construction can be made operational without circularity, the result would meaningfully extend reject-option methods beyond aleatoric uncertainty to handle epistemic uncertainty, which is relevant for high-stakes applications with scarce data. The approach of redefining the predictor via expected regret is conceptually clean and could support falsifiable abstention rules, but its practical value hinges on whether regret is estimable from finite samples.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (method): The redefinition of the optimal predictor as minimizing expected regret to the Bayes-optimal predictor is stated, but no derivation or expression is supplied showing how this regret is computed or bounded using only quantities observable from the finite training set and the learned posterior; without such an expression the abstention threshold cannot be evaluated in practice.
  2. [§4] §4 (estimation): The assumption that regret relative to the unknown Bayes-optimal predictor can be meaningfully estimated from the limited-data model is load-bearing for the framework, yet the manuscript provides no concrete estimator, bound, or consistency argument that avoids reducing to quantities already fitted from the same data.
minor comments (2)
  1. [§2] Notation for the rejection cost and the regret functional should be introduced with explicit definitions early in the paper to avoid ambiguity when the abstention rule is stated.
  2. [Abstract] The abstract claims this is the 'first principled framework'; a short related-work paragraph contrasting with existing epistemic-uncertainty or selective-prediction methods would strengthen the positioning.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments correctly identify that the manuscript emphasizes the conceptual framework but requires additional detail on practical computation and estimation to be fully operational. We address each point below and will incorporate the necessary clarifications and derivations in the revised version.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (method): The redefinition of the optimal predictor as minimizing expected regret to the Bayes-optimal predictor is stated, but no derivation or expression is supplied showing how this regret is computed or bounded using only quantities observable from the finite training set and the learned posterior; without such an expression the abstention threshold cannot be evaluated in practice.

    Authors: We agree that an explicit derivation is needed for the abstention rule to be evaluable. While §3 defines the optimal predictor via expected regret to the Bayes-optimal predictor, the manuscript does not supply the intermediate steps for computing this from the posterior. In the revision we will add a derivation in §3 expressing the expected regret as an integral over the posterior predictive distribution, which depends only on the learned posterior and the finite training data. This will yield a computable bound or approximation for the regret that directly determines the abstention threshold. revision: yes

  2. Referee: [§4] §4 (estimation): The assumption that regret relative to the unknown Bayes-optimal predictor can be meaningfully estimated from the limited-data model is load-bearing for the framework, yet the manuscript provides no concrete estimator, bound, or consistency argument that avoids reducing to quantities already fitted from the same data.

    Authors: We acknowledge that a concrete estimator and supporting argument are required to establish that the approach is non-circular. The current §4 focuses on the high-level estimation strategy but does not detail a specific procedure or consistency result. In the revision we will expand §4 with a Monte Carlo estimator that samples from the posterior to approximate the regret, together with a consistency argument showing convergence to the true regret as the posterior concentrates. This estimator uses the model's own posterior rather than re-fitting to the same data, thereby addressing the concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper proposes a conceptual redefinition of the optimal predictor via expected regret to the Bayes-optimal predictor (with full distributional knowledge) under a Bayesian learning setup, then uses this to define an abstention rule when regret exceeds a rejection cost. This is presented as a definitional framework for handling epistemic uncertainty rather than a derived claim that reduces by construction to fitted parameters or prior self-citations. No equations or load-bearing steps in the abstract or description exhibit a reduction where a 'prediction' or result is equivalent to its own inputs (e.g., no fitted regret estimate renamed as a first-principles output, no uniqueness theorem imported from overlapping authors, and no ansatz smuggled via citation). The derivation remains self-contained as a theoretical proposal building on established Bayesian principles without evident circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework depends on Bayesian modeling of epistemic uncertainty and the ability to define and estimate regret without direct access to the true distribution.

free parameters (1)
  • rejection cost
    Threshold value that determines abstention when expected regret exceeds it; chosen or tuned for the application.
axioms (2)
  • domain assumption Bayesian learning can quantify epistemic uncertainty from limited training data
    Invoked to distinguish epistemic from aleatoric uncertainty and to support regret calculation.
  • domain assumption Expected regret can be computed or approximated from the learned model
    Central to redefining the optimal predictor and the abstention rule.

reviewed 2026-05-18 · how reviews work

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Cite this review

Pith. "Pith review of Epistemic Reject Option Prediction." pith.science (2026). https://pith.science/paper/2511.04855

@misc{pith2026251104855,
  author       = {Pith},
  title        = {Pith review of: Epistemic Reject Option Prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2511.04855}},
  note         = {Machine review of arXiv:2511.04855}
}
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read the original abstract

In high-stakes applications, predictive models must not only produce accurate predictions but also quantify and communicate their uncertainty. Reject-option prediction addresses this by allowing the model to abstain when prediction uncertainty is high. Traditional reject-option approaches focus solely on aleatoric uncertainty, an assumption valid only when large training data makes the epistemic uncertainty negligible. However, in many practical scenarios, limited data makes this assumption unrealistic. This paper introduces the epistemic reject-option predictor, which abstains in regions of high epistemic uncertainty caused by insufficient data. Building on Bayesian learning, we redefine the optimal predictor as the one that minimizes expected regret -- the performance gap between the learned model and the Bayes-optimal predictor with full knowledge of the data distribution. The model abstains when the regret for a given input exceeds a specified rejection cost. To our knowledge, this is the first principled framework that enables learning predictors capable of identifying inputs for which the available training data is insufficient to support well-informed predictions.

Figures

Figures reproduced from arXiv: 2511.04855 by Jakub Paplham, Vojtech Franc.

Figure 1
Figure 1. Figure 1: The aleatoric reject-option predictor outputs [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Fig 2a illustrates the Bayesian reject-option predictor (14), which outputs the prediction [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The performance of different reject-option pre [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    redefine the optimal predictor as the one that minimizes expected regret – the performance gap between the learned model and the Bayes-optimal predictor with full knowledge of the data distribution. The model abstains when the regret for a given input exceeds a specified rejection cost.

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supports
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extends
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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Evaluating Epistemic Uncertainty: Beyond OOD Detection and Active Learning

    cs.LG 2026-07 conditional novelty 6.0

    Epistemic uncertainty should be judged by how well it ranks reducible error, and a new Pareto-gap diagnostic shows proxy-task rankings can invert.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · cited by 1 Pith paper

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This paper was first reviewed by grok-4.3 on May 18, 2026.