Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem.

Conformal prediction is a framework for predictive inference with a distributionfree, finite-sample guarantee. However, it tends to provide uninformative prediction sets when calibration data are scarce. This paper introduces Synthetic-powered predictive inference (SPI), a novel framework that incorporates synthetic data-- e.g., from a generative model--to improve sample efficiency. At the core of our method is a score transporter: an empirical quantile mapping that aligns nonconformity scores from trusted, real data with those from synthetic data. By carefully integrating the score transporter into the calibration process, SPIprovably achieves finite-sample coverage guarantees without making any assumptions about the real and synthetic data distributions. When the score distributions are well aligned, SPIyields substantially tighter and more informative prediction sets than standard conformal prediction. Experiments on image classification--augmenting data with synthetic diffusion-model generated images--and on tabular regression demonstrate notable improvements in predictive efficiency in data-scarce settings.

Visual In-Context Learning (VICL) has emerged as a prominent approach for adapting visual foundation models to novel tasks, by effectively exploiting contextual information embedded in in-context examples, which can be formulated as a global ranking problem of potential candidates. Current VICL methods, such as Partial2Global and VPR, are grounded in the similarity-priority assumption that images more visually similar to a query image serve as better in-context examples. This foundational assumption, while intuitive, lacks sufficient justification for its efficacy in selecting optimal in-context examples. Furthermore, Partial2Global constructs its global ranking from a series of randomly sampled pairwise preference predictions. Such a reliance on random sampling can lead to incomplete coverage and redundant samplings of comparisons, thus further adversely impacting the final global ranking. To address these issues, this paper introduces an enhanced variant of Partial2Global designed for reliable and holistic selection of in-context examples in VICL. Our proposed method, dubbed RH-Partial2Global, leverages a jackknife conformal prediction-guided strategy to construct reliable alternative sets and a covering design-based sampling approach to ensure comprehensive and uniform coverage of pairwise preferences. Extensive experiments demonstrate that RH-Partial2Global achieves excellent performance and outperforms Partial2Global across diverse visual tasks.

Personalized federated learning addresses data heterogeneity across distributed agents but lacks uncertainty quantification that is both agent-specific and instancespecific, which is a critical requirement for risk-sensitive applications. We propose personalized federated conformal prediction (PFCP), a novel framework that combines personalized federated learning with conformal prediction to provide statistically valid agent-personalized prediction sets with instance-localization. By leveraging privacy-preserving knowledge transfer from other source agents, PFCP ensures marginal coverage guarantees for target agents while significantly improving conditional coverage performance on individual test instances, which has been validated by extensive experiments.

Existing approaches either neglect dependencies, leading to overly conservative predictions, or rely solely on data-driven estimations, failing to capture the rich topological structure of the network. To address these challenges, we propose Spatio-Temporal Adaptive Conformal Inference (STACI), a novel framework that integrates network topology and temporal dynamics into the conformal prediction framework. STACIintroduces a topology-aware nonconformity score that respects directional flow constraints and dynamically adjusts prediction sets to account for temporal distributional shifts. We provide theoretical guarantees on the validity of our approach and demonstrate its superior performance on both synthetic and real-world datasets. Our results show that STACIeffectively balances prediction efficiency and coverage, outperforming existing conformal prediction methods for stream networks.

Automatic summarization systems have advanced rapidly with large language models (LLMs), yet they still lack reliable guarantees on inclusion of critical content in high-stakes domains like healthcare, law, and finance. In this work, we introduce Conformal Importance Summarization, the first framework for importance-preserving summary generation which uses conformal prediction to provide rigorous, distribution-free coverage guarantees. By calibrating thresholds on sentence-level importance scores, we enable extractive document summarization with user-specified coverage and recall rates over critical content. Our method is model-agnostic, requires only a small calibration set, and seamlessly integrates with existing black-box LLMs. Experiments on established summarization benchmarks demonstrate that Conformal Importance Summarization achieves the theoretically assured information coverage rate. Our work suggests that Conformal Importance Summarization can be combined with existing techniques to achieve reliable, controllable automatic summarization, paving the way for safer deployment of AI summarization tools in critical applications.

Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by modeling distribution shifts using Lévy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations. We provide a self-contained overview of LP ambiguity sets and their connections to popular metrics such as Wasserstein and Total Variation. We show that the link between conformal prediction and LP ambiguity sets is a natural one: by propagating the LP ambiguity set through the scoring function, we reduce complex high-dimensional distribution shifts to manageable onedimensional distribution shifts, enabling exact quantification of worst-case quantiles and coverage. Building on this analysis, we construct robust conformal prediction intervals that remain valid under distribution shifts, explicitly linking LP parameters to interval width and confidence levels. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach.

We study the problem of uncertainty quantification for time series prediction, with the goal of providing easy-to-use algorithms with formal guarantees. The algorithms we present build upon ideas from conformal prediction and control theory, are able to prospectively model conformal scores in an online setting, and adapt to the presence of systematic errors due to seasonality, trends, and general distribution shifts. Our theory both simplifies and strengthens existing analyses in online conformal prediction. Experiments on 4-week-ahead forecasting of statewide COVID-19 death counts in the U.S. show an improvement in coverage over the ensemble forecaster used in official CDC communications. We also run experiments on predicting electricity demand, market returns, and temperature using autoregressive, Theta, Prophet, and Transformer models.

Conformal prediction is an emerging technique for uncertainty quantification that constructs prediction sets guaranteed to contain the true label with a predefined probability. Recent work develops online conformal prediction methods that adaptively construct prediction sets to accommodate distribution shifts. However, existing algorithms typically assume perfect label accuracy which rarely holds in practice. In this work, we investigate the robustness of online conformal prediction under uniform label noise with a known noise rate. We show that label noise causes a persistent gap between the actual mis-coverage rate and the desired rate α, leading to either overestimated or underestimated coverage guarantees. To address this issue, we propose a novel loss function robust pinball loss, which provides an unbiased estimate of clean pinball loss without requiring ground-truth labels. Theoretically, we demonstrate that robust pinball loss enables online conformal prediction to eliminate the coverage gap under uniform label noise, achieving a convergence rate of O(T 1/2) for both empirical and expected coverage errors (i.e., absolute deviation of the empirical and expected mis-coverage rate from the target level α). This loss offers a general solution to the uniform label noise, and is complementary to existing online conformal prediction methods. Extensive experiments demonstrate that robust pinball loss enhances the noise robustness of various online conformal prediction methods by achieving a precise coverage guarantee and improved efficiency.

Uncertainty quantification (UQ) is essential for safe deployment of generative AI models such as large language models (LLMs), especially in high-stakes applications. Conformal prediction (CP) offers a principled uncertainty quantification framework, but classical methods focus on regression and classification, relying on geometric distances or softmax scores-tools that presuppose structured outputs. We depart from this paradigm by studying CP in a query-only setting, where prediction sets must be constructed solely from finite queries to a black-box generative model, introducing a new trade-off between coverage, test-time query budget, and informativeness. We introduce Conformal Prediction with Query Oracle (CPQ), a framework characterizing the optimal interplay between these objectives. Our finite-sample algorithm is built on two core principles: one governs the optimal query policy, and the other defines the optimal mapping from queried samples to prediction sets.