arxiv: 2605.01452 · v1 · submitted 2026-05-02 · 📊 stat.ME · cs.LG

Recognition: unknown

Stable Localized Conformal Prediction via Transduction

Yinjie Min , Liuhua Peng , Changliang Zou

Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:06 UTC · model grok-4.3

classification 📊 stat.ME cs.LG

keywords conformal predictionstabilitytransfer learningtransductionprediction setsmarginal coveragelocalized methodscalibration data

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The pith

Transfer learning from source tasks produces more stable conformal prediction sets with limited calibration data.

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

Standard conformal prediction can yield highly variable prediction set sizes from a single small calibration set, especially when the method localizes intervals. The paper defines set stability as the variance of the conditional expectation of set size given the calibration data. It introduces Stable Conformal Prediction (StCP), a transduction approach that borrows labeled source-task data together with unlabeled target data. Theory establishes marginal coverage and improved stability; experiments confirm lower variability than standard methods, most clearly for localized procedures.

Core claim

We propose Stable Conformal Prediction (StCP), a transfer learning approach that utilizes labeled source-task data and unlabeled target data. We characterize the marginal coverage and stability of StCP; empirically, it delivers more stable prediction sets than standard conformal prediction methods, especially for those with localization, when calibration data are limited.

What carries the argument

The StCP transduction procedure that incorporates labeled source data through unlabeled target samples to reduce variance in conformal set sizes.

If this is right

Marginal coverage on the target task remains valid.
Variability of prediction set size conditional on calibration data is reduced.
Stability gains are largest for localized conformal methods.
No additional target-task labels beyond the usual calibration set are needed.

Where Pith is reading between the lines

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

Similar transduction could be tested on other uncertainty methods that suffer from small-sample instability.
Domains with abundant related source data but scarce target labels may achieve reliable localized intervals with smaller calibration budgets.
Empirical studies across more task pairs would map the similarity conditions that produce the largest stability improvements.

Load-bearing premise

Source-task data must be related enough to the target task that the transferred labels improve stability without breaking marginal coverage.

What would settle it

An experiment that repeatedly draws small calibration sets from the target distribution and checks whether StCP fails to produce lower variance in set sizes than standard conformal prediction while still achieving nominal coverage.

Figures

Figures reproduced from arXiv: 2605.01452 by Changliang Zou, Liuhua Peng, Yinjie Min.

**Figure 1.** Figure 1: Effects of n on the prediction efficiency and stability. tions PX and P ′ X may differ substantially, the conditional distributions PY |X and P ′ Y |X are similar. Under this setup, we propose a general transductive framework to stabilize conformal prediction while preserving core predictive properties. Our contributions are as follows: (i) We propose Stable Conformal Prediction (StCP), a general stabili… view at source ↗

**Figure 2.** Figure 2: Workflow of StCP. provides a stability-oriented choice under the tolerance constraint. Finally, define CbSt-sel(Xn+1) = {y : S(Xn+1, y) ≤ qbSt-sel}. That is, we construct the final StCP set using the selected parameter λb. 4. Theoretical Analysis First, we show that StCP preserves satisfactory marginal coverage. When λ = 0, the optimization problem in (7) reduces to directly aligning Fb1 S (·; Fe S|X) wit… view at source ↗

**Figure 3.** Figure 3: Sensitivity to λ under the LogAbs setting view at source ↗

**Figure 4.** Figure 4: Additional λ sensitivity results under the Quad and Softplus settings. The Quad setting exhibits the strongest variance reduction for the GLCP-type method, while the Softplus setting follows a smoother trajectory. 22 view at source ↗

read the original abstract

Existing evaluations of conformal prediction, such as prediction efficiency and test-conditional coverage, are defined in expectation over the calibration data. In practice, when only one calibration set of limited size is available, prediction sets often exhibit high variability in size, especially for methods with localization. We formalize this concern as set stability, defined as the variance of the conditional expectation of the set size given the calibration data. To improve stability without requiring additional target-task labels, we propose Stable Conformal Prediction (StCP), a transfer learning approach that utilizes labeled source-task data and unlabeled target data. Theoretically, we characterize the marginal coverage and stability of StCP; empirically, it delivers more stable prediction sets than standard conformal prediction methods, especially for those with localization, when calibration data are limited.

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.

Desk Editor's Note private letter to a colleague

The paper defines set stability as variance in expected prediction-set size given the calibration data and proposes StCP to reduce that variance via transduction from labeled source data plus unlabeled target data.

read the letter

The central contribution is formalizing set stability for conformal prediction and showing a transduction route to improve it. They treat stability as the variance of E[set size | calibration set] and build StCP by combining source labels with target unlabeled points to produce more consistent set sizes, especially for localized scores when the target calibration set is small. The abstract claims they characterize both marginal coverage and the resulting stability, and the empirical section reportedly shows gains over standard CP in that regime. That focus on practical variability with one fixed calibration draw is useful; most CP work optimizes average efficiency or conditional coverage but leaves the single-realization fluctuation unaddressed. The transfer step is a straightforward way to borrow strength without new target labels. The soft spot is the implicit requirement that source and target are close enough for the mixed calibration to preserve the quantile properties that deliver coverage. If the score distributions differ materially, the stability improvement can come at the cost of coverage or can simply fail to appear. The abstract does not report explicit bounds on allowable shift or experiments that sweep over relatedness, so the characterization may not yet rule out degradation under realistic mismatches. This is for researchers who already work with conformal methods in limited-data settings and are willing to assume or check source-target similarity. It is worth sending to peer review because the stability definition is new, the practical problem is real, and the proposed fix is simple enough that referees can evaluate the coverage claims directly.

Referee Report

2 major / 3 minor

Summary. The paper proposes Stable Conformal Prediction (StCP), a transduction-based transfer learning approach that combines labeled source-task data with unlabeled target-task data to reduce the variance of prediction set sizes (formalized as set stability) in conformal prediction, especially for localized methods under limited calibration data. It claims to characterize the marginal coverage and stability of StCP theoretically and demonstrates empirically that it yields more stable sets than standard conformal prediction baselines.

Significance. If the central claims hold, the work addresses a practically relevant limitation of conformal prediction—the high variability of set sizes with small calibration sets—by leveraging transfer learning without requiring extra target labels. The theoretical characterization of both coverage and stability, together with the empirical focus on localized methods, represents a clear strength and could influence downstream applications in settings with heterogeneous data sources.

major comments (2)

[§3.2 and Theorem 1] §3.2 (Transduction step) and Theorem 1: The marginal coverage guarantee is derived under an implicit assumption that the source and target score distributions are sufficiently related for the combined calibration set to preserve the quantile properties. However, the paper does not quantify the allowable shift (e.g., via total variation or density ratio bounds) nor show that coverage degradation remains controlled when this relatedness is only approximate; the mixture of source and target scores can alter the effective quantile, undermining the claimed exact marginal coverage.
[§4] §4 (Stability analysis): The variance reduction claim for Var(E[set size | calibration set]) is shown under the transduction construction, but the derivation does not bound the additional variability introduced by the source-target mismatch. When the source distribution differs in local density, the stability gain can become negative, yet no sensitivity analysis or worst-case bound is provided to support the central stability improvement claim.

minor comments (3)

[§3.1] The notation for the transduction weights in Eq. (7) is introduced without an explicit statement of how they are estimated from the unlabeled target data; a short algorithmic box would improve clarity.
[Table 2] Table 2: The reported standard deviations for set size are computed over only 10 random splits; increasing this to 50–100 would better substantiate the stability comparison.
[§1.2] Related work on transfer conformal prediction (e.g., methods using importance weighting) is cited but not compared in the experiments; a brief discussion of why transduction was chosen over reweighting would help readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which identify key points for clarifying our theoretical results on coverage and stability. We respond point by point below.

read point-by-point responses

Referee: [§3.2 and Theorem 1] §3.2 (Transduction step) and Theorem 1: The marginal coverage guarantee is derived under an implicit assumption that the source and target score distributions are sufficiently related for the combined calibration set to preserve the quantile properties. However, the paper does not quantify the allowable shift (e.g., via total variation or density ratio bounds) nor show that coverage degradation remains controlled when this relatedness is only approximate; the mixture of source and target scores can alter the effective quantile, undermining the claimed exact marginal coverage.

Authors: Theorem 1 establishes exact marginal coverage under the assumption that the combined calibration scores (from source and target) are exchangeable with the test score. This holds precisely when the nonconformity scores share the same distribution, which is ensured by the relatedness between source and target tasks as formalized in the transduction construction of §3.2. We did not include explicit shift bounds because the result is stated for the exact-exchangeability case. We will revise the statement of Theorem 1 and the surrounding discussion in §3.2 to make the exchangeability assumption explicit and add a remark noting that coverage becomes approximate under distribution shift, with a brief reference to how total-variation distance between score distributions would control the deviation. revision: yes
Referee: [§4] §4 (Stability analysis): The variance reduction claim for Var(E[set size | calibration set]) is shown under the transduction construction, but the derivation does not bound the additional variability introduced by the source-target mismatch. When the source distribution differs in local density, the stability gain can become negative, yet no sensitivity analysis or worst-case bound is provided to support the central stability improvement claim.

Authors: The variance reduction in §4 is derived for the specific transduction estimator that augments the target calibration set with source scores. We agree that large mismatches in local density can offset or reverse the stability gain. The analysis focuses on the regime where source and target are related enough for the empirical gains shown in the experiments. We will add a sensitivity subsection to §4 that provides a first-order bound on the extra variability induced by score-distribution mismatch (via the difference in local densities) and states the conditions under which the net stability improvement remains positive. revision: partial

Circularity Check

0 steps flagged

No circularity: new transduction method with independent theoretical characterization

full rationale

The paper introduces StCP as a transfer-learning extension of conformal prediction that combines labeled source data with unlabeled target data to stabilize set sizes. Its central claims rest on a fresh definition of set stability (variance of conditional expected set size) and a new transduction procedure whose marginal coverage and stability are derived from first principles under the stated exchangeability assumptions. No equation reduces a prediction or coverage guarantee to a fitted parameter or prior self-citation by construction; the derivation chain is self-contained and externally falsifiable via the usual conformal coverage arguments plus the explicit source-target relatedness assumption.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract, no specific free parameters or invented entities mentioned; standard conformal assumptions likely apply.

axioms (1)

domain assumption Standard assumptions for conformal prediction such as exchangeability of data points
Conformal prediction relies on this for coverage guarantees.

pith-pipeline@v0.9.0 · 5423 in / 1010 out tokens · 45601 ms · 2026-05-09T18:06:56.308594+00:00 · methodology

discussion (0)

Reference graph

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