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arxiv: 2606.18199 · v1 · pith:DRRD44NFnew · submitted 2026-06-16 · 🧮 math.ST · q-fin.RM· stat.ME· stat.ML· stat.TH

Conformal Prediction Intervals with Tail-Specific Guarantees

Simone Cuonzo , Nina Deliu This is my paper

Pith reviewed 2026-06-26 21:44 UTC · model grok-4.3

classification 🧮 math.ST q-fin.RMstat.MEstat.MLstat.TH
keywords conformal predictionprediction intervalstail-specific coveragemarginal coverageexchangeable datanon-exchangeable datasplit conformal predictiondirectional calibration
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The pith

Conformal prediction intervals can be built to guarantee calibrated coverage separately in the upper and lower tails while preserving global marginal coverage.

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

The paper constructs two-sided prediction intervals by intersecting lower and upper one-sided conformal intervals, each calibrated for marginal coverage. This yields intervals that control the probability of errors in each tail direction individually, in addition to the usual overall coverage level. The guarantees hold exactly for exchangeable data and asymptotically for non-exchangeable observations. Simulations indicate better performance on skewed distributions compared with standard two-sided conformal intervals. The framework is illustrated on a financial task that requires strict left-tail control alongside return maximization.

Core claim

By taking the intersection of a lower one-sided conformal interval and an upper one-sided conformal interval, each constructed to achieve its own marginal coverage, the resulting two-sided interval inherits explicit tail-specific coverage guarantees together with the global marginal coverage of 1 minus alpha. Finite-sample validity holds under exchangeability; asymptotic validity holds for non-exchangeable sequences.

What carries the argument

Intersection of one-sided conformal intervals that each achieve marginal coverage.

If this is right

  • The two-sided interval maintains coverage of at least 1-alpha globally while also covering the lower tail and upper tail at their respective calibrated levels.
  • Finite-sample tail-specific guarantees apply whenever the data are exchangeable.
  • Asymptotic tail-specific guarantees apply to non-exchangeable data sequences.
  • Directional calibration improves on skewed distributions relative to classical two-sided conformal intervals.
  • The construction supports applications that require asymmetric tail control, such as financial return maximization with left-tail risk limits.

Where Pith is reading between the lines

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

  • The same intersection construction could be applied to other conformal methods that produce one-sided intervals.
  • In settings with strong dependence, the asymptotic results may still require verification on the specific dependence structure.
  • When tail costs are highly asymmetric, the separate calibration allows explicit trade-offs between upper and lower coverage levels that standard intervals do not expose.
  • The method extends naturally to multivariate responses if one-sided conformal bounds can be defined coordinate-wise.

Load-bearing premise

The building-block one-sided conformal intervals achieve their claimed marginal coverage.

What would settle it

An exchangeable dataset in which the empirical frequency that observations fall below the lower endpoint of the two-sided interval is strictly less than the claimed tail level, while the one-sided lower interval itself meets its marginal guarantee.

Figures

Figures reproduced from arXiv: 2606.18199 by Nina Deliu, Simone Cuonzo.

Figure 1
Figure 1. Figure 1: Comparison of lower-tail coverage (left panels) and prediction intervals (right [PITH_FULL_IMAGE:figures/full_fig_p027_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of upper-tail coverage over time for SPY, TQQQ, and XLE obtained [PITH_FULL_IMAGE:figures/full_fig_p052_2.png] view at source ↗
read the original abstract

This paper extends classical conformal frameworks for constructing prediction intervals with global marginal coverage $1-\alpha$ to intervals that provide explicitly calibrated guarantees for the upper and lower tails separately. Focusing on split conformal prediction, we first construct lower and upper one-sided conformal intervals that achieve marginal validity, and then derive the induced two-sided interval by intersection. Theoretical results prove both tail-specific and global marginal coverage of the induced two-sided interval. Results are presented first for the exchangeable setting, where coverage has finite-sample guarantees, and then for non-exchangeable data, where guarantees are asymptotic. Simulation studies show that the proposed approach achieves improved directional calibration relative to classical two-sided intervals, especially relevant in skewed data. Finally, the benefit of the proposed framework is showcased in a financial application, where one aims for return maximization while seeking strict control on the left tail.

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 paper extends split conformal prediction to construct two-sided intervals that deliver explicit marginal coverage guarantees separately for the lower tail (P(Y < L) ≤ α) and upper tail (P(Y > U) ≤ α), in addition to the usual global coverage ≥ 1−2α. One-sided split conformal intervals are built as building blocks and the two-sided interval is obtained by their intersection. Finite-sample validity is claimed under exchangeability; asymptotic validity is claimed for non-exchangeable data under standard regularity conditions. Simulations are reported to show improved directional calibration versus classical two-sided conformal intervals (especially on skewed data), and a financial application is presented for return maximization with left-tail control.

Significance. If the derivations hold, the contribution supplies a simple, assumption-light way to obtain tail-specific control within the conformal framework. This is practically relevant for risk-sensitive domains such as finance. The finite-sample guarantees under exchangeability and the explicit use of the union-bound argument for global coverage are clear strengths; the simulation evidence on skewed distributions further supports utility. The approach does not introduce new free parameters or invented entities beyond standard conformal machinery.

minor comments (1)
  1. The abstract states that the two-sided interval is formed by intersection of one-sided intervals; a brief explicit statement of the resulting coverage statements (e.g., via union bound) in the main text would improve readability for readers unfamiliar with the construction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, significance assessment, and recommendation to accept the manuscript. No major comments were raised, so we have no points to address.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation begins from the established finite-sample marginal coverage property of one-sided split conformal intervals under exchangeability (a standard result independent of this paper) and forms the two-sided interval by intersection. Tail-specific bounds and the global coverage guarantee then follow directly from the one-sided properties via the union bound, without any redefinition, parameter fitting presented as prediction, or load-bearing self-citation. The asymptotic non-exchangeable extension likewise invokes only routine regularity conditions from the conformal literature. All steps are self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard exchangeability assumption of conformal prediction plus the validity of one-sided conformal intervals; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Data points are exchangeable (any permutation equally likely) for finite-sample coverage guarantees
    Explicitly stated in the abstract for the exchangeable setting.

pith-pipeline@v0.9.1-grok · 5676 in / 1144 out tokens · 20031 ms · 2026-06-26T21:44:41.160138+00:00 · methodology

discussion (0)

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Reference graph

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