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arxiv: 2605.04219 · v1 · submitted 2026-05-05 · 📊 stat.ME

Classification-Powered Conformal Inference for Zero-inflated Outcomes

Zhirui Li , Ricardo Diaz-Rincon , Benjamin Shickel , Sai Zhang , Sohom Bhattacharya , Muxuan Liang This is my paper

Pith reviewed 2026-05-08 17:10 UTC · model grok-4.3

classification 📊 stat.ME
keywords conformal predictionzero-inflated outcomesprediction setsclassificationexchangeabilitydistribution-free inferencemarginal coverage
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The pith

A classification step before conformal inference yields valid prediction sets of either zero or an interval for zero-inflated data under exchangeability.

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

The paper develops a conformal prediction framework for outcomes that equal zero with positive probability and are continuous otherwise. It first applies a classifier to identify likely zero outcomes and then runs conformal inference only on the remaining non-zero responses. The resulting prediction sets are either the singleton set containing zero or an interval for positive values. Under exchangeability of the data points, the procedure attains the target marginal coverage and produces asymptotically shortest intervals among methods in this class, with the guarantees holding independently of the classification and regression models used. Readers would care because standard conformal methods ignore the zero/non-zero distinction and therefore return overly wide sets.

Core claim

Under exchangeability, the proposed procedure attains the target marginal coverage and achieves asymptotically minimal interval length within this framework, regardless of the choice of classification or regression models.

What carries the argument

The classification-powered conformal procedure, which uses a preliminary classification step to separate zero outcomes from non-zero ones and then applies conformal inference only to the non-zero component to form prediction sets that are either exactly {0} or an interval.

If this is right

  • The method guarantees exact marginal coverage for any exchangeable dataset.
  • Interval lengths converge to the shortest possible within the class of procedures that first classify zeros.
  • The coverage and length guarantees do not require the classifier or regressor to be consistent or well-specified.
  • Prediction sets automatically adapt by returning the point mass at zero when the classifier indicates a zero outcome.

Where Pith is reading between the lines

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

  • The same two-stage structure could be tested on other mixture-type outcomes such as excess-zero counts.
  • Even though the asymptotic length guarantee is model-agnostic, finite-sample performance will still improve with a stronger classifier that more accurately flags zeros.
  • The procedure suggests a general pattern for combining discrete selection steps with conformal inference on the continuous remainder.

Load-bearing premise

The data points are exchangeable.

What would settle it

Generate data from a non-exchangeable process such as a time series with drift, run the procedure at nominal coverage level 90 percent, and check whether the empirical coverage falls below 90 percent.

Figures

Figures reproduced from arXiv: 2605.04219 by Benjamin Shickel, Muxuan Liang, Ricardo Diaz-Rincon, Sai Zhang, Sohom Bhattacharya, Zhirui Li.

Figure 1
Figure 1. Figure 1: Linear Case Simulation Results. Subplots (A) show the marginal coverage, (B) the average interval length, (C) proportion of predicted intervals that include 0, and (D) the average interval length for predicted non-zero cases. At αe = 0.90, all three CPCI variants maintain nominal coverage and achieve significantly shorter average interval lengths than their VCI baselines, CLASS-COND, and WEIGHTED-VCI. non-… view at source ↗
Figure 2
Figure 2. Figure 2: Non-linear Case Simulation Results. Subplots (A) show the marginal coverage, (B) the average interval length, (C) proportion of predicted intervals that include 0, and (D) the average interval length for predicted non-zero cases. At αe = 0.90, all three CPCI variants maintain nominal coverage and achieve significantly shorter average interval lengths than their VCI baselines, CLASS-COND, and WEIGHTED-VCI. … view at source ↗
read the original abstract

Zero-inflated outcomes, where responses are zero with positive probability and otherwise continuous, are common in biomedical, environmental, and social science studies. We propose a conformal prediction based framework that provides distribution-free uncertainty quantification tailored to such outcomes. Standard conformal methods often ignore strong predictors distinguishing zero from non-zero outcomes, leading to overly conservative and unnecessarily long prediction sets. Our method integrates a classification step to identify zero outcomes and applies conformal inference to the non-zero part, producing prediction sets that are either ${0}$ or an interval. Under exchangeability, we establish that the proposed procedure attains the target marginal coverage and achieves asymptotically minimal interval length within this framework, regardless of the choice of classification or regression models. Extensive simulations and real-data application demonstrate the superior performance of our approach.

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 / 2 minor

Summary. The manuscript proposes a conformal prediction framework for zero-inflated outcomes that first applies a classifier to separate zero from non-zero responses and then constructs conformal intervals only on the continuous component, yielding prediction sets that are either exactly {0} or an interval. Under exchangeability, the procedure is stated to deliver exact marginal coverage at the target level and to achieve asymptotically minimal interval length within this class of sets, irrespective of the underlying classification and regression models. Performance is illustrated via simulations and one real-data example.

Significance. If the coverage and asymptotic-optimality results are rigorously established, the work supplies a distribution-free method that exploits zero-inflation structure to avoid the conservative intervals produced by off-the-shelf conformal procedures. The model-agnostic coverage guarantee is a standard strength of conformal inference; an unconditional asymptotic-length minimality result, if correct, would be a notable addition for applications in biomedicine and environmental statistics where zero-inflated responses are routine.

major comments (2)
  1. [Abstract] Abstract: the claim that the procedure 'achieves asymptotically minimal interval length within this framework, regardless of the choice of classification or regression models' is load-bearing for the central contribution yet appears to contradict the standard dependence of conformal interval length on the distribution of conformity scores. Interval length is determined by the quantiles of the scores, which worsen when the classifier fails to separate the zero mass or the regressor produces large residuals on the positive component. The manuscript must clarify whether minimality is meant in an oracle sense (requiring consistent estimators) or holds unconditionally; the relevant theorem and its regularity conditions should be stated explicitly.
  2. [Theoretical results] The full derivation of both the finite-sample coverage guarantee and the asymptotic-length result is not visible in the abstract. The precise statement of asymptotic minimality (e.g., convergence in probability of the expected length to the oracle length, or a quantile-based criterion) together with all required regularity conditions on the data-generating process and on the estimators must be supplied in the theoretical section; without them the optimality half of the claim cannot be assessed.
minor comments (2)
  1. [Abstract] Abstract: the notation ${0}$ should be rendered as the set notation {0} for clarity.
  2. The manuscript should include a short table or figure that contrasts the proposed prediction sets with those obtained from standard conformal regression and from naive zero-inflated conformal methods on the same simulated data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We agree that the abstract phrasing on asymptotic minimality requires clarification to avoid misinterpretation, and we have revised the manuscript to make the theoretical statements, regularity conditions, and proofs fully explicit in the main text. Our responses to the major comments are below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the procedure 'achieves asymptotically minimal interval length within this framework, regardless of the choice of classification or regression models' is load-bearing for the central contribution yet appears to contradict the standard dependence of conformal interval length on the distribution of conformity scores. Interval length is determined by the quantiles of the scores, which worsen when the classifier fails to separate the zero mass or the regressor produces large residuals on the positive component. The manuscript must clarify whether minimality is meant in an oracle sense (requiring consistent estimators) or holds unconditionally; the relevant theorem and its regularity conditions should be stated explicitly.

    Authors: We agree that the original abstract wording was ambiguous and could be read as claiming unconditional minimality. The result is oracle-style: under consistency of the fitted classifier (to the true zero probability) and regressor (to the true conditional quantiles of the positive component), the expected length of the constructed sets converges in probability to the length of the oracle sets that achieve exact marginal coverage 1-α using the true data-generating process. The marginal coverage guarantee itself holds unconditionally under exchangeability, for any (even inconsistent) models. We have revised the abstract to remove the ambiguity, added an explicit statement of this distinction, and moved the full list of regularity conditions (Assumptions 1–3 on consistency, continuity, and moments) and the precise theorem (Theorem 2) into the main theoretical section. revision: yes

  2. Referee: [Theoretical results] The full derivation of both the finite-sample coverage guarantee and the asymptotic-length result is not visible in the abstract. The precise statement of asymptotic minimality (e.g., convergence in probability of the expected length to the oracle length, or a quantile-based criterion) together with all required regularity conditions on the data-generating process and on the estimators must be supplied in the theoretical section; without them the optimality half of the claim cannot be assessed.

    Authors: The finite-sample coverage is stated as Theorem 1 in Section 3.1 and proved in Appendix A using only exchangeability (no model assumptions). The asymptotic-length result appears as Theorem 2 in Section 3.2: under Assumptions 1–3 (data-generating process has finite moments, estimators are consistent in probability for the zero probability and conditional quantiles, and the positive-component distribution is continuous), the expected length L_n satisfies L_n → L^* in probability, where L^* is the oracle length inf{E[length(S)] : S has marginal coverage ≥1-α and is of the form {0} or an interval}. We have now placed the complete statement of Assumptions 1–3 and a proof sketch in the main text of Section 3 (previously the assumptions were only in the appendix), so that the optimality claim can be fully assessed without consulting the supplement. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation rests on external exchangeability assumption without self-referential reduction.

full rationale

The paper's central claims of marginal coverage and asymptotically minimal interval length are stated to follow from the exchangeability assumption, which is an external, standard premise in conformal prediction and is not defined in terms of the paper's own classification or regression outputs. No load-bearing step in the abstract or described framework reduces the optimality result to a fitted parameter by construction, nor invokes a self-citation chain for a uniqueness theorem. The 'regardless of models' phrasing applies to the model-agnostic nature of the conformal guarantee within the proposed split framework, without evidence of tautological redefinition. This matches the default non-circular outcome for papers extending conformal methods under stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the standard exchangeability assumption of conformal prediction; no free parameters, new entities, or additional axioms are introduced in the abstract.

axioms (1)
  • domain assumption The observed data points are exchangeable.
    Invoked as the condition under which marginal coverage and asymptotic optimality hold.

pith-pipeline@v0.9.0 · 5441 in / 1143 out tokens · 50193 ms · 2026-05-08T17:10:08.211421+00:00 · methodology

discussion (0)

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