localized conformal prediction

This work addresses conformal prediction under the challenging setting of *unlabeled calibration data*, proposing the first general framework that achieves statistically valid coverage guarantees without requiring any labeled samples. Methodologically, it leverages unlabeled data to estimate a surrogate calibration score and derives a verifiable coverage bound by incorporating the model’s accuracy (or a precision metric). Theoretically, the resulting prediction set satisfies a finite-sample coverage guarantee: $mathbb{P}(Y in C) geq 1 - alpha - eta$. The framework is unified across both classification and regression tasks, eliminating the conventional reliance on labeled calibration sets. This breakthrough significantly broadens the applicability of conformal prediction to low-resource, privacy-sensitive, and high-label-cost scenarios. Moreover, it delivers a plug-and-play uncertainty quantification solution with rigorous statistical guarantees.

Standard conformal prediction guarantees only marginal coverage, failing to ensure conditional coverage for critical subgroups—such as high-confidence misclassified samples or sensitive demographic groups. To address this, we propose a novel conformal calibration framework that jointly leverages classifier confidence scores and nonparametric trust scores. This work is the first to incorporate trust scores into conformal prediction, replacing conventional univariate calibration with bivariate quantile calibration over the “confidence + trust” score pair. Our method comprises three components: nonparametric trust estimation, extension of marginal conformal prediction, and a joint calibration mechanism. Extensive evaluation across multiple image datasets demonstrates that our approach improves class-conditional coverage by 12–28%, enhances stability of subgroup and sensitive-group coverage, and reduces coverage deviation by over 40%. These gains significantly improve model fairness and reliability—particularly under data scarcity.

In online learning settings, existing multi-model conformal prediction methods lack theoretical guarantees for model selection and aggregation. Method: This paper proposes the first online conformal model aggregation framework based on temporal weighted voting, integrating conformal prediction, online learning, and an empirical coverage-driven weight update mechanism to enable real-time, adaptive adjustment of model weights. The framework rigorously maintains $1-alpha$ marginal coverage while dynamically optimizing prediction set quality. Contribution/Results: Unlike conventional paradigms requiring a pre-specified single model, our approach supports seamless integration of heterogeneous model streams. Evaluated on multiple data stream benchmarks, it significantly reduces average prediction set width—achieving both statistical reliability (via guaranteed coverage) and practical utility (via tighter, adaptive intervals).

Conformal prediction for multi-class classification often suffers from inefficiency and overly large prediction sets due to reliance on a single scoring function. To address this, we propose a weighted ensemble of multiple scoring functions within the conformal prediction framework. Our method learns data-driven weights via joint optimization grounded in empirical risk minimization, integrating Vapnik–Chervonenkis (VC) theory with convex optimization. Crucially, we establish, for the first time, a theoretical connection between weighted score aggregation and VC subgraph classes—thereby enabling provably optimal multi-score fusion. Under strict coverage guarantees (e.g., 90%), our approach significantly reduces prediction set size, achieving an average reduction of 12.6% across multiple benchmark datasets. It consistently outperforms state-of-the-art single-score conformal methods in both efficiency and predictive performance.

Conventional conformal prediction is limited to single-point predictions, failing to quantify uncertainty for aggregate statistics—such as class-wise mean accuracy or total path cost—defined over arbitrary index sets. Method: We propose the first extension of conformal prediction to joint interval estimation of sums or means of unknown labels across arbitrary index sets. Our symmetrically calibrated conformalized interval arithmetic framework ensures exact marginal coverage under permutation invariance, relaxing the single-target constraint without distributional assumptions. Contribution/Results: The method is theoretically rigorous and computationally tractable. Experiments on class-average estimation and path-cost prediction demonstrate that it achieves exact nominal coverage while yielding significantly tighter intervals than state-of-the-art conformal and non-conformal baselines, establishing new performance benchmarks for multi-label uncertainty quantification.

This work addresses the limitation of traditional conformal prediction, which guarantees only marginal coverage and often exhibits poor conditional coverage, leading to calibration bias in specific regions of the covariate space. To overcome this, the authors propose Randomized Localized Conformal Prediction (RLCP), a method that performs local calibration within neighborhoods of test points, thereby enhancing conditional coverage while preserving marginal validity. The paper establishes, for the first time, finite-sample, high-probability uniform guarantees for such localized approaches, simultaneously controlling both conditional coverage error and oracle length error. By leveraging Hölder continuity, kernel density estimation, data-splitting-based score learning, and conformal quantile regression, the authors develop a theoretical framework for local coverage, deriving finite-sample bounds on the conditional coverage gap and length error, and demonstrating that improved score estimation enables performance approaching that of the oracle.

This work addresses the challenge of unreliable prediction sets in regions with sparse calibration data, where existing local conformal prediction (LCP) methods struggle to maintain validity. The paper proposes Enhanced Local Conformal Prediction (ELCP), which, for the first time, effectively incorporates imperfect auxiliary information into the LCP framework under potential distribution shift. ELCP employs a density ratio–weighted kernel estimator to construct more reliable local prediction sets. While preserving finite-sample marginal coverage guarantees, the method substantially improves local coverage performance. Experimental results demonstrate that, under limited calibration data, ELCP achieves higher local coverage rates and yields significantly tighter prediction sets compared to standard LCP.

This work addresses a key limitation of traditional conformal prediction, which guarantees only marginal coverage without independent control over upper and lower tail risks. The authors propose a novel split-conformal approach that constructs one-sided prediction intervals—each marginally valid for its respective tail—and derives a two-sided interval via their intersection. This framework provides, for the first time, finite-sample or asymptotic guarantees of tail-specific coverage. By moving beyond the conventional focus on overall coverage, the method significantly improves directional calibration in simulations with skewed data and enables practical applications such as financial portfolio optimization, where it effectively supports return maximization while rigorously controlling left-tail risk.

This study addresses the challenge of constructing confidence intervals for the expectation of a target variable within the observed sample in small-area estimation. The authors propose a novel conditional conformal inference method that, under exchangeability or i.i.d. assumptions and within a regression framework, achieves finite-sample valid inference for the in-sample mean—a task previously unattainable with standard conformal prediction, which is inherently designed for out-of-sample prediction. By conditioning appropriately on the observed data, the proposed approach yields confidence intervals that rigorously maintain the prescribed coverage probability even when the underlying regression model is misspecified, thereby extending the applicability of conformal inference to internal estimation problems while preserving its nonparametric reliability guarantees.

Standard conformal prediction struggles to guarantee reliable coverage under outliers or heavy-tailed distributions. This work proposes a novel nonconformity scoring method based on the half-sample radius—the distance to the (⌊n/2⌋+1)-th nearest neighbor—thereby introducing geometric robustness into the conformal prediction framework for the first time. The method satisfies marginal validity in finite samples and converges at an exponential rate to the population center set defined by a distance-based functional. Rigorous theoretical analysis yields sharp tail deviation bounds, ensuring both theoretical guarantees and practical robustness for heavy-tailed or multimodal distributions.