Conformal Prediction

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Latest papers 334

55 papers in the last four weeks, up 57% on the four weeks before. 0.3% of all new papers.

Aug 23, 2026

CS-WCP: Robust Conformal Sets for LLM-Judge Traffic Shifts with Uncertain Group Proportions

Prediction sets built from an LLM judge can undercover when deployment traffic changes the prevalence of task or policy groups. Weighted conformal prediction is exact under covariate shift when the density ratio is known, but group proportions must usually be estimated from finite unlabeled samples. We introduce confidence-set weighted conformal prediction (CS-WCP), which constructs simultaneous exact intervals for source and target group masses and returns the union of weighted conformal sets over every compatible ratio vector. For a fixed or independently learned finite partition, CS-WCP attains coverage at least 1-alpha-delta_w-tau_A-kappa, where tau_A measures within-cell covariate mismatch and kappa measures conditional shift. A linear endpoint rule computes the robust union in O(G|Y|) time. Across 336 constructed shared-support traffic shifts, CS-WCP reaches 0.973 mean coverage with 13 point failures, compared with 0.954 and 44 failures for source conformal prediction, at mean binary set sizes 1.74 and 1.65. On 336 natural cross-task transfers, coverage rises from 0.882 to 0.962, but mean set size reaches 1.87 and a size-matched group plug-in baseline is competitive. The method therefore supplies an auditable coverage safeguard under uncertain mixture weights; its value is conservative tail protection, not scalar probability calibration or uniformly smaller sets.

Ibne Farabi Shihab, Fariya Afrin

Department of Computer Science, Iowa State University · Department of Computer Science, Kalinga Institute of Industrial Technology

Conformal Prediction Weighted Conformal Prediction Distribution Shift Robustness Covariate Shift

Aug 21, 2026

Reaching the Tail: Calibration Diversity Drives Conformal Coverage under Data Scarcity

Multi-horizon rare-event forecasting is hard under long macroeconomic series' data constraints: labeled events are scarce, and standard uncertainty quantification assumes an exchangeability that autocorrelation violates. A controlled ablation shows an apparent rare-event threshold for Adaptive Conformal Inference instead reflects calibration-set size. Across 200 random calibration sets, support width of the nonconformity-score distribution explains up to 85% of coverage variance versus 2% for rare-event count; the same, not the same magnitude, replicates across synthetic conditions and five countries (five-country Spearman

ρ

0.45-0.66 vs. 0.02-0.23). A diversity-maximizing selector built on this is the only strategy tested that improves long-horizon coverage (67.8% to 81.4% at six months); Mondrian, shift-robust, and extreme-value alternatives fail to close it. Mondrian even worsens coverage under oracle labels. A compact proposition explains why: coverage deficit reflects how closely the calibration set's upper quantile reaches the test distribution's. Diversity is necessary, not sufficient. Demonstrated on a two-stage U.S. recession-forecasting framework with RegressorChain, whether six-month coverage reaches 90% under honest scoring remains open, a question this paper quantifies rather than resolves.

Donald Aadithiyan

Department of Computer Science and Engineering, University of Moratuwa, Moratuwa, Sri Lanka

Conformal Prediction Adaptive Conformal Inference Data Selection Financial Forecasting

Aug 21, 2026

SPARC: Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layers

Human motion forecasters are increasingly accurate and fast, but reliable deployment requires uncertainty estimates that are structured, calibrated, and efficient. Bayesian and ensemble-based uncertainty estimates often require repeated stochastic inference [15, 26], while conformal calibration alone does not provide an epistemic signal or preserve trajectory covariance structure [14, 50]. We introduce SPARC (Single-Pass Adaptive Risk Calibration), a Bayesian-conformal uncertainty layer for motion forecasting. A deterministic MLP backbone predicts the future mean, and a conjugate Bayesian last layer converts time-domain feature leverage into an analytic horizon-wise epistemic scale

κ_t(x)

. This scale inflates a graph-temporal Gaussian covariance without changing its correlation structure, and split conformal calibration produces 95% marginal prediction tubes with finite-sample validity under exchangeability. The key interface is the structured factorization

κ_t(x)Σ_{\mathrm{str},t}(x)

, which injects feature-space epistemic uncertainty into trajectory densities without Monte Carlo sampling. Across nine dataset-protocol blocks and deterministic, multimodal, and calibration baselines, SPARC ranks first on NLL and on the combined MPJPE+NLL criterion while retaining competitive point accuracy and efficient calibrated tubes. Ranking windows by

κ

separates high-error cases, making the scale usable as a lightweight risk monitor.

Sakif Hossain, Julian Teusch, Jörg P. Müller

Clausthal University of Technology (TU Clausthal)

Human Motion Prediction Uncertainty Calibration Epistemic Uncertainty Conformal Prediction Bayesian Inference

Aug 21, 2026

CAS: Conformalized Agentic Search via Adaptive Retrieval and Policy Weighting

Search Agents face a severe reliability crisis during reinforcement learning (RL) fine-tuning. Heuristic Top-K retrieval often causes critical evidence loss or noise inclusion, while over-confidence induced by progressive RL leads to hallucinated answers and redundant searches. To build highly reliable agents, we introduce Conformal Prediction (CP) and propose Conformalized Agentic Search (CAS). This framework establishes reliability guarantees on both the retrieval and training sides: on the retrieval side, an Adaptive Prediction Set (APS), a specific CP realization, translates statistical coverage into dynamic document truncation to construct prediction sets that are adaptive in size; on the training side, Adaptive Conformal Inference (ACI), a dynamic CP algorithm, dynamically constructs prediction sets with controllable coverage to quantify answer confidence, which is then used to penalize low-confidence trajectories within the Group Relative Policy Optimization (GRPO) objective, ensuring the model learns only from reliable ones. Experiments across single-hop and multi-hop QA datasets demonstrate that our framework significantly improves reasoning accuracy while drastically reducing redundant tool invocations, establishing a highly reliable and efficient agent paradigm. Our code is available at https://github.com/S1llyBird/CAS.

Zixi Zhu, Jiayuan Su, Jian Zhang +2

ZJU-UIUC Institute, Zhejiang University. · Tencent Inc. · State Key Laboratory of CAD&CG, Zhejiang University.

Agentic Search LLM Agent Reliability RL for LLM Agents Adaptive Retrieval Conformal Prediction

Aug 19, 2026

Does Marginal Coverage Guarantee Class-Conditional Safety for Zero-Shot VLMs Under Shift?

Split-conformal prediction provides marginal coverage under exchangeability and is increasingly used as an abstention layer for zero-shot vision-language models (VLMs). We audit this practice under deployment shift for CLIP, OpenCLIP, and SigLIP across ImageNet and non-ImageNet settings. Marginal coverage can remain relatively high while class-conditional tail coverage collapses: on ImageNet-Sketch, worst-class coverage falls to

\approx 0

and 10-12% of classes lie below a finite-sample null floor, despite marginal coverage of about 0.86. The failure is aligned with target-domain class accuracy but is not predicted by the source-domain diagnostics we test. Source-side Mondrian calibration improves the in-distribution tail but does not transfer, while clustered conformal and Conf-OT improve marginal or average metrics without recovering the worst-class tail. Target-side class calibration substantially lifts the tail, but requires labels for every class and remains set-size-intensive. We further identify a 2-3

\times

cross-family efficiency gap and show that native SigLIP sigmoid scores remove APS's probability-mass interpretation. The findings persist across the tested model scale, pretraining corpus, prompt, miscoverage level

α

, and shifted non-ImageNet settings. Marginal conformal coverage should therefore be treated as an average reliability statistic, not as a safety guarantee for the class tail.

Jai Kumar Sharma, Amartya Dutta

Virginia Tech, Blacksburg, VA, USA

Conformal Prediction VLM Evaluation VLM Robustness Group-Conditional Conformal Prediction Zero-Shot Learning

Aug 19, 2026

When Clean Signals Are Not Enough: Detecting Structural Ambiguity for Safe Wearable Stress Classification

Wearable stress classifiers can achieve strong average performance while failing completely for a particular individual. On WESAD, a Random Forest reaches 93.0% mean accuracy yet yields F1 = 0 for Subject 14, whose cross-signal coupling weakens near stress onset. We call this structural ambiguity: individually plausible physiological channels form an inter-signal pattern that is poorly supported by the person's non-stress reference. We introduce the Individual Conformal Coupling Monitor (ICCM), a lightweight and transparent pre-inference monitor that quantifies subject-specific coupling divergence and routes each window to classify, defer, or abstain without retraining the downstream classifier. Across WESAD (N = 15) and Stress-Predict (N = 35), full-cohort Pearson associations between ambiguity and accuracy are negative (r = -0.607, p = 0.016; r = -0.412, p = 0.014). Robustness analyses temper this finding: rank correlations are not significant, and the WESAD association disappears when Subject 14 is removed. ICCM changes false-positive counts from 29 to 27 and 94 to 92, although neither paired change is significant. It withholds 3 of Subject 14's 21 stress windows but does not repair the missed-stress failure. These results position ICCM as an interpretable signal of unsupported physiology and individual failure, rather than a stand-alone safety guarantee.

Saba A. Farahani, Hung Cao, Amir M. Rahmani

University of California, Irvine Irvine, CA, USA

Wearable Health Monitoring Selective Prediction Conformal Prediction

Aug 18, 2026

Conformal Prediction for Molecular Properties under Label Shift

Drug discovery and development underpins healthcare but remains costly and failure-prone. A critical bottleneck lies in predicting molecular properties such as solubility, potency, and toxicity, which directly determine whether a candidate can advance from preclinical to clinical trials. Artificial Intelligence (AI) has accelerated this process, yet its reliability is often undermined by distribution shift, as experimental conditions frequently diverge from training data. In addition, conventional point predictions provide only single-value estimates, offering limited guidance for high-stakes experimental design. We address these challenges with a conformal prediction framework tailored to label shift. By weighting conformal scores using marginal label probability ratios, our method produces statistically rigorous prediction intervals without retraining. This enables robust uncertainty quantification even when property distributions drift, directly tackling one of the most pervasive obstacles to applying AI in real-world drug development. By moving beyond accuracy alone to provide actionable confidence measures, our approach enhances the trustworthiness of AI-driven predictions. This further aligns predictive modeling with regulatory demands for transparency and uncertainty reporting and ultimately supports more reliable decision-making in billion-dollar development pipelines.

Hyeonsu Lee, Juyeon Kim, Erkhembayar Jadamba +2

Mogam Institute for Biomedical Research · Intellicode

Conformal Prediction Label Shift Regression Prediction Intervals Weighted Conformal Prediction Molecular Property Prediction

Aug 18, 2026

SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting

Modern probabilistic time-series forecasters often express uncertainty through forecast samples. While typically converted into nominal prediction regions using empirical quantiles, these model-implied sets lack formal coverage guarantees and frequently deviate from nominal targets under distribution shift. Existing multivariate conformal methods can calibrate these regions online, but they typically estimate geometry from historical residuals using fixed or accumulating look-back windows. This reliance on the past limits their ability to exploit the instantaneous dependence structure of current predictions and leaves them vulnerable to stale-regime contamination. To address this, we propose SPACE, a conformal wrapper for sample-generating multivariate forecasters. SPACE constructs ellipsoidal joint prediction regions by estimating time-local covariance geometry directly from the current forecast sample cloud, calibrating the region's radius via a dynamic backward window-selection scheme. Across diverse multivariate datasets, probabilistic forecasters, and conformal baselines, SPACE consistently brings realized joint and rolling coverage closer to the nominal target, achieving superior coverage-efficiency tradeoffs relative to competing wrappers.

Baishi Li, Kelvin J. L. Koa, Ke-Wei Huang

Department of Information Systems and Analytics, National University of Singapore · Asian Institute of Digital Finance, National University of Singapore

Conformal Prediction Multivariate Time Series Forecasting Probabilistic Time Series Forecasting Adaptive Conformal Inference

Aug 16, 2026

Temporal Graph Prototype-conditioned Conformal Prediction for Fraud Detection

Conformal prediction (CP) provides distribution-free coverage guarantees and has emerged as a principled tool for uncertainty quantification. In edge-level fraud detection on temporal interaction graphs, where false positives and false negatives both carry substantial cost, such coverage guarantees are particularly appealing for risk-aware decision making. However, directly applying existing graph conformal predictors yields inefficient prediction sets due to two recurring properties of fraud data. Fraudulent interactions are often embedded in benign-dominated neighborhoods that dilute calibration signals, while extreme class imbalance leaves scarce labeled-fraud support in the calibration split and leads to overly conservative class-conditional thresholds. To address these issues, we propose ProtoCP, a conformal prediction framework for edge-level fraud detection on temporal graphs. ProtoCP improves calibration efficiency by focusing calibration on fraud-relevant subgraph context and producing more stable nonconformity scores under class imbalance and temporal drift. Specifically, it leverages learned prototypes to suppress benign-dominated noise in the calibration context and introduces a neighborhood-relative scoring mechanism with temporal score diffusion for stable class-conditional calibration. Experiments on four fraud benchmarks (YelpChi, S-FFSD, FTFD, and BankSim) show that ProtoCP achieves the target coverage with consistently smaller prediction sets than state-of-the-art baselines. Our codes are available at https://github.com/Picard1701ent/ProtoCP.git

Xudong Chen, Shengbo Gong, Lu Cheng +1

Emory University Atlanta, USA · University of Illinois at Chicago Chicago, IL, USA

Conformal Prediction Financial Fraud Detection

Aug 15, 2026

SCORE: Shape-Conforming Regions for Flight in Enclosed, Degraded Environments

Autonomous UAVs enter enclosed environments such as caves and collapsed structures that confine the vehicle and degrade perception. Conformal prediction provides a distribution-free guarantee by calibrating how far an obstacle keep-out must expand to absorb perception error at a target coverage level. However, existing keep-out regions use convex primitives whose bulges consume narrow passages and grow as perception degrades. Our main contribution defines the nonconformity score on a signed distance field (SDF). This produces a non-convex keep-out that tightly follows obstacle geometry and avoids the unnecessary bulging of equal-margin convex regions. Two supporting components keep this geometry usable as perception degrades. First, a voxelwise union of complementary sensor observations certifies voxels that any single sensor misses. Second, the margin around the obstacle adapts to measured visibility without weather labels or the online ground-truth feedback that single-pass flight cannot provide. Results on real subterranean data show that the resulting distribution-free, shape-conforming keep-out retains more usable free space than convex baselines at the same certified coverage, and produces safer closed-loop flight.

Eric Minwoo Kim, Jong-Kook Kim

School of Electrical Engineering, Korea University, Seoul, Republic of Korea

UAV Navigation Robotics Robot Motion Planning Conformal Prediction

Aug 12, 2026

Confidence Calibration of Deep Learning Systems

In high-stakes applications, reliable confidence estimates are as important as the predictions themselves. Confidence calibration ensures that predicted probabilities reflect the likelihood of correctness, making it essential for safe deployment of deep learning models. However, existing methods typically assume access to clean validation data, which is often unrealistic due to label noise and domain shifts. This thesis develops methods for improving calibration under these conditions. First, we address calibration under label noise. Standard methods can produce misleading confidence estimates when labels are unreliable. We propose a framework that uses an estimated noise model to reconstruct noise-free confidence estimates by modeling the relationship between noisy and clean label distributions. We extend this approach to Conformal Prediction (CP), which provides set-valued predictions with guaranteed coverage. Our noise-aware CP method estimates clean conformity scores despite label noise, enabling reliable uncertainty quantification. Next, we study calibration in unsupervised domain adaptation, where a model trained on a labeled source domain is adapted to an unlabeled target domain. Since labeled target data are unavailable, we estimate target-domain accuracy from source performance and domain discrepancies, enabling calibration without target labels. We also consider privacy-preserving settings in which user labels and model outputs must remain protected. We propose a locally differentially private conformal prediction framework that provides valid uncertainty quantification while maintaining privacy guarantees and balancing privacy, computational feasibility, and prediction reliability. Our results bridge calibration theory and practical deployment in safety-critical applications, contributing to reliable, privacy-preserving, and noise-resilient neural network predictions.

Coby Penso

The Faculty of Engineering, Bar-Ilan University, Ramat Gan, Israel

Unsupervised Domain Adaptation Conformal Prediction Model Calibration Uncertainty Calibration

Aug 11, 2026

Retrieval-Corrected Conformal Prediction for Time Series

Conformal prediction (CP) provides distribution-free prediction intervals for fixed forecasters, but its standard calibration procedure is often inefficient for time series data, where forecast errors are temporally dependent and change across time and operating conditions. Recent time series CP methods improve local calibration using recent, weighted, or localized residuals. Yet local calibration can remain indirect, since broad residual weighting or additional adaptation procedures may dilute the evidence most relevant to the current prediction. This motivates a simple retrieval and correction strategy that selects similar past residuals as local evidence and then corrects the coverage error left by retrieval. In this paper, we propose Retrieval--Corrected Conformal Prediction (RCCP), a retrieval-augmented calibration method for time series prediction intervals. RCCP builds an asymmetric interval from retrieved one-sided residuals and calibrates its normalized retrieval error with a scalar conformal correction. Thus, retrieval provides local residual evidence, while conformal correction determines the final scale needed for coverage. We provide a coverage-gap bound based on the stability of the normalized retrieval error distribution. Across standard benchmarks and backbone forecasters, RCCP attains the target coverage in every setting and achieves the lowest Winkler scores, with fewer severe misses. RCCP also achieves low calibration and inference overhead, showing that retrieval-corrected calibration is an effective and scalable approach to uncertainty quantification in time series forecasting. Code is available at https://github.com/jinsaaang/rccp.

Sangjin Jin, Kangmin Kim, Junhyeong Lee +1

Ulsan National Institute of Science and Technology Ulsan, Republic of Korea

Time Series Forecasting Conformal Prediction Uncertainty Calibration Regression Prediction Intervals

Aug 10, 2026

Particle-Based Conformal Prediction for Contact-Aware Uncertainty Calibration in Stratified Configuration Spaces

Reliable uncertainty representation is essential for deploying autonomous systems that interact with their environment, as robots must reason about how uncertainty arising from both stochasticity and model mismatch is impacted by contacts with obstacles (e.g., when navigating through a cluttered environment or inserting a part into an assembly). We propose Calibrated Particle-sets for Trans-dimensional Uncertainty Representation (CaPTURe), a geometry-aware, conformal prediction-based algorithm that generates probabilistically valid prediction regions of the unknown future system configuration using particle-based models of arbitrary fidelity. While calibrated uncertainty predictions are essential for safe and efficient planning, analytical or learned motion models are often inaccurate - due to limited data, simplifying assumptions, unmodeled effects, etc. - which can lead to unsafe executions or task failure. Additionally, when a robot contacts an obstacle, the distribution of its future configurations can become multimodal or disjoint, or lie along manifolds of lower intrinsic dimension than the space of possible robot configurations. Our method uses a calibration dataset of system transitions to locally calibrate motion uncertainty estimates, constructing regions guaranteed to contain the future robot configuration at a user-set probability. Our calibration procedure captures how motion uncertainty varies between contact-rich and contactless motions, leading to sufficient coverage in both cases. We evaluate our method on two simulated planning tasks: controlling a marble around a labyrinth and performing tight-tolerance peg-in-hole insertion with a manipulator. Compared to relevant baselines, CaPTURe achieves the user-specified coverage requirement both in and out of contact and achieves up to a 30% absolute improvement in task success rate over the best baseline.

Luís Marques, Kristian Popov, Dmitry Berenson

Department of Robotics, University of Michigan, Ann Arbor, MI, 48109, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

Contact-Rich Robotic Manipulation Conformal Prediction Safe Motion Planning Robot Motion Planning Uncertainty Calibration

Aug 9, 2026

ARC: Augmented-Rank Conformalization for Changepoint Localization --- Finite-Sample Validity and Distribution-Robust Efficiency

Conformal changepoint localization turns any score into a confidence set for the changepoint with finite-sample coverage. Coverage is universal; efficiency is not. The oracle score is a likelihood ratio, so practical scores estimate density ratios, and set length deteriorates under heavy tails, skewness, and distribution shift, where no length guarantee applies. We propose ARC (Augmented-Rank Conformalization), a family of scores depending on the data only through within-segment ranks: rank-CUSUM location and scale channels, their fixed combinations, and a lightweight neural score frozen after synthetic training. Every ARC score inherits finite-sample coverage for every frozen weight configuration, including random initialization and mistraining. The main result is an efficiency transfer theorem: the entire ARC confidence set is almost surely invariant under strictly increasing marginal transforms, so the set length distribution depends on the data pair only through its rank structure, and lengths certified once hold verbatim across its monotone orbit, whereas a plug-in score's length changes with every re-expression. Across different rank structures lengths do change, and are reported as such. Classical rank-test theory positions ARC as targeting the optimal invariant score at bounded cost. Simulations confirm nominal coverage for all scores, including sabotaged networks, identical sets under monotone transforms where plug-in scores inflate, and smooth degradation where plug-in sets become vacuous; on the well-log benchmark ARC localizes annotated shifts to three to five candidates and flags misfit by an empty set. Two boundaries are stated rather than hidden: serial dependence destroys exactness, and trend-type alternatives lie outside the piecewise-exchangeable model.

Chenchen Peng, Mixia Wu, Qijing Yan +2

School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China · College of Computing and Data Science, Nanyang Technological University, Singapore 639798, Singapore

Confidence Region Estimation Conformal Prediction Change-Point Detection

Aug 7, 2026

CoCoNav: Conformal Control for Safe Robot Navigation in Crowds

Safe and efficient robot navigation in crowds requires anticipating pedestrian motion despite uncertain and potentially shifting prediction errors. Existing reactive methods can produce oscillatory behavior, while predictive planners often treat forecasts as exact or rely on restrictive error models. Incorporating conservative uncertainty sets as hard constraints can also render model predictive control (MPC) infeasible. We propose CoCoNav, a crowd-navigation framework that combines online conformal calibration with runtime-certified planning. A horizon-specific conformal proportional--integral controller adapts trajectory-error bounds to regulate long-run empirical coverage, enabling the framework to respond to changing prediction errors. A relax-then-verify planner preserves solver feasibility by generating nominal trajectories with soft-constrained MPC and separately certifying them, together with contingency maneuvers, against the calibrated bounds before execution. Simulations and quadruped experiments show that CoCoNav achieves a favorable balance among collision avoidance, task success, and navigation efficiency relative to the evaluated baselines.

Cheng Guo, Mingzhe Ni, Zheng Liang +5

Department of Computer Science, The University of Manchester, Manchester, UK. · Human-Robot Interfaces and Interaction Laboratory, Italian Institute of Technology, Genoa, Italy. · Genisom AI, Shanghai, China. +3

Constrained Motion Planning Conformal Prediction Safe Robot Navigation Social Robot Navigation Robot Safety Model Predictive Control+1

Aug 7, 2026

Conformal Coverage Guarantees for Any Video Temporal Grounder

Event boundaries in continuous video are ambiguous: re-annotate the same query-video pair and independent annotators mark moments that overlap by less than half on a large fraction of samples. The ground truth for video temporal grounding is therefore a distribution over intervals, yet every grounder returns a single interval with no statement of reliability, so at deployment a wrong interval is indistinguishable from a right one. COVER changes the output object: a post-hoc, model-agnostic wrapper that turns any grounder, a trained localizer or a black-box video--language model, into one that emits a temporal region containing the true moment with probability at least

1-α

, by calibrating the quantile of a temporal nonconformity score on held-out labels and widening the base prediction by that amount. The guarantee is finite-sample and distribution-free under exchangeability, and requires neither retraining nor white-box access. We give two score families, a two-sided boundary-widening score for grounders that emit an interval and a super-level-set score for grounders that emit a relevance signal, and develop theory specific to grounding that bounds how large the certified region becomes, when coverage survives conditioning on event length, and how it degrades when moments from one video break exchangeability. Across three benchmarks and five grounders, realized coverage tracks the target, and calibration exposes what point metrics hide.

Aseel Mohamed, Rasul Khanbayov, Erchin Serpedin +1

Department of Electrical and Computer Engineering, Texas A&M University at Qatar, Doha, Qatar · College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar · Department of Computer and Electrical Engineering, Texas A&M University, College Station, TX, USA

Temporal Video Grounding Uncertainty Quantification Conformal Prediction

Aug 7, 2026

Conformal Fusion Under Missing Modalities

Multimodal fusion architectures typically assume all modalities are available at inference, yet sensor failures, acquisition variability, and cost constraints routinely produce incomplete observations. Existing work treats modality absence as a prediction-accuracy problem, leaving a more basic question unanswered: whether a model's confidence estimates remain calibrated when an entire input stream is removed. We argue that missing-modality robustness and calibrated uncertainty are a single coupled property, and introduce Modality-Conditioned Conformal Fusion (MCCF), an architecture that addresses both at once. MCCF combines a multimodal bottleneck fusion backbone trained with modality dropout, per-modality evidential heads producing modality-decomposed Dirichlet distributions, and a Dempster-Shafer combination rule that fuses the per-modality evidence into a joint predictive distribution; an absent modality contributes vacuous evidence that is structurally ignored, so the fused uncertainty automatically reflects the reduced information without test-time imputation. A Mondrian conformal calibration module keyed on the modality-presence mask then provides finite-sample group-conditional coverage for every non-empty modality subset. MCCF is, to our knowledge, the first method with formal coverage guarantees under arbitrary modality availability through architectural integration rather than post-hoc recalibration, and the evidential decomposition yields per-modality vacuity scores that localise uncertainty to the absent modality responsible. Across a synthetic problem and three real multimodal benchmarks, MCCF holds its target coverage on every modality-presence subset, substantially narrows the coverage gap between full and partial modalities relative to a marginal split-conformal baseline, and imposes no measurable accuracy cost relative to temperature-scaled and evidential baselines.

Alireza Moayedikia

Department of Business Technology and Entrepreneurship Swinburne University of Technology Hawthorn, VIC 3122, Australia

Missing-Modality Learning Group-Conditional Conformal Prediction Dempster-Shafer Theory Conformal Prediction Uncertainty-Aware Multimodal Fusion Multimodal Fusion+1

Aug 7, 2026

Online Conformal Prediction Beyond Feedback

Online conformal prediction (OCP) provides theoretically principled uncertainty quantification for arbitrary black-box classifiers and non-i.i.d. data streams by constructing prediction sets that are guaranteed to contain the true label at a user-specified frequency. OCP usually updates prediction sets using feedback from previously deployed predictions. We instead study an OCP setting beyond feedback: on each round, the learner can either output a prediction set or query the correct label, but not both. Thus, no deployed prediction is ever evaluated directly. We reduce this problem to a partial monitoring game in which prediction actions return no observation and a separate query action reveals the label. To solve this game, we develop OCP with queries (OCPQ), a label-efficient forecasting algorithm designed for this beyond-feedback setting. Using an adequate reward construction, for any black-box classifier and any (non-i.i.d.) oblivious data stream of length

T

, OCPQ has

O(T^{2/3})

expected regret and expected coverage of at least

β-O(T^{-1/3})

for a user-defined

β

, while querying only an expected

T^{-1/3}

fraction of rounds. This provides coverage comparable to bandit-based OCP methods while requiring no feedback from deployed predictions. Experiments on real-world datasets demonstrate the effectiveness of our approach.

Joar Skalse, Edoardo Pona, Osvaldo Simeone +1

King’s College London · Northeastern University London

Uncertainty Quantification Conformal Prediction

Aug 6, 2026

CertBind from Multimodal Connectivity to Certifiable Retrieval Decisions

Lightweight connectors make frozen multimodal encoders composable at the representation level. Deployment exposes a second problem at the level of task decisions. A connected route can expand cross-modal reach while changing an established native retrieval capability. We introduce CertBind, a multiscale theory of certifiable composition for frozen multimodal connector graphs. At the node scale, native anchors establish the exact task identification boundary under the stated chart model. At the edge scale, contract-aware conformal ranks provide graph-wide family-wise error control. At the path scale, an overlap-aware budget and clean calibration yield a finite-sample recovery radius under declared conditions. At the query scale, this radius yields a covered top-k candidate set that becomes a point certificate when its size equals k. CertBind therefore retains supported routes as Direct, sends only flagged routes to recovery, returns Certified for decisive recovery, and returns Abstain for unresolved queries. The evaluated C-MCR shared route reduced native CLIP R@1 from 0.524 to 0.290. The production fallback recovered 0.963 +- 0.002 of clean retrieval, while the passing branch recorded a no-harm value of 1.000. CertBind extends multimodal composability from connected representations to certifiable task decisions.

Shuheng Cao, Zhenhao Zhang, Ruiqi Chen +7

University of California, San Diego · ShanghaiTech University · Tsinghua University +5

Selective Prediction Conformal Prediction Cross-Modal Retrieval Information Retrieval

Aug 6, 2026

Beyond Marginal Validity: Finite-Sample Guarantees for Localized Conformal Prediction

Conformal prediction endows arbitrary black-box predictors with finite-sample, distribution-free marginal coverage, yet marginal validity can hide severe covariate-specific miscalibration, while exact distribution-free conditional coverage is finite-sample unattainable. Randomly localized conformal prediction (RLCP) mitigates this gap by calibrating near the test point while preserving marginal coverage. Existing theory, however, lacks finite-sample guarantees for the realized localized set that jointly control conditional validity and oracle efficiency. We provide such guarantees. For any fixed score, under Hölder regularity of the conditional score CDF and standard density and kernel assumptions, we prove high-probability bounds, uniform over a realized localization neighbourhood, for the conditional-coverage gap and the length error relative to the oracle. The bounds decompose into an

O(h^β)

localization bias and a calibration term decreasing with calibration size, clarifying the bandwidth bias-variance tradeoff and when RLCP tracks the oracle. We also analyze data-split learned scores: when the score targets a pivotal score, as in conformalized quantile regression, uniform local guarantees decompose into fixed-score calibration and uniform score-estimation errors, showing that improved learning sharpens localized guarantees.

Anton Conrad, Rustam Isaev, Denis Belomestny +2

Laboratoire de Recherche d’EPITA, 14–16 rue Voltaire, 94276 Le Kremlin-Bicêtre CEDEX, France · Faculty of Computer Science, HSE University, 11 Pokrovsky Boulevard, Moscow 109028, Russia · Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 1 Leninskie Gory, Building 52, Moscow 119991, Russia +2

Conformal Prediction Statistical Learning Theory

Aug 5, 2026

Hybrid Probabilistic Zonotopes for Identifiable and Refinable Predictive Uncertainty

Probabilistic prediction heads in neural networks typically output either a Gaussian mixture or a single conformal region. Neither separates the distinct sources of uncertainty often present in real prediction tasks: a discrete choice among modes, bounded systematic drift within the chosen mode, and irreducible stochastic noise. We introduce the Hybrid Probabilistic Zonotope (HProbZ), an output head that represents these three sources as binary, bounded, and stochastic generators of a zonotope, and admits a closed-form likelihood by convolution. Sharing the bounded generator across prediction steps couples future predictions algebraically, so observing one step refines the predictive distribution at every remaining step in a single forward pass. We establish that the three generators are identifiable from the likelihood up to permutation, and that an HProbZ density is representationally distinct from any finite Gaussian mixture. The same shared structure provides analytic per-mode risk and distribution-free multi-modal conformal sets at inference time. Empirical analysis on representative prediction benchmarks supports the effectiveness of the design relative to same-encoder mixture baselines, while offering structural properties that mixture or convex-conformal predictors do not jointly provide.

Zhen Zhang, Amr Alanwar

School of Computation, Information and Technology, Technical University of Munich, Germany

Uncertainty Quantification Probabilistic Forecasting Conformal Prediction Uncertainty Decomposition

Aug 5, 2026

Distribution-Free Conformal Prediction for Steel Fatigue Strength: Marginal Validity Is Not Enough

Predicting fatigue failure in steel components experimentally is costly because it requires testing across multiple compositions and processing conditions. This has spurred research on data-driven prediction models. Studies using the NIMS MatNavi steel fatigue dataset often report high point-prediction accuracy but rely on aggregate error metrics, leaving uncertainty about the reliability of individual predictions and whether accuracy is consistent across the fatigue-strength spectrum. This paper is the first to apply conformal prediction to steel fatigue strength, comparing five interval-construction methods across 50 independent data splits and distinguishing marginal coverage from coverage within specific sub-regions of the predicted property. A gradient-boosting point model achieves an R^2 of 0.976 +/- 0.009 and a mean absolute error of 18.3 +/- 2.3 MPa. Split-conformal prediction provides valid marginal coverage (0.918) but drops to 0.755 in the highest-strength quartile, where design margins are most critical, a pattern also observed with a Gaussian process baseline. A cross-fitted, normalized conformal method restores near-uniform coverage across all quartiles (0.869-0.938) without a significant increase in interval width, by scaling the interval based on a cross-fitted estimate of local prediction difficulty rather than using a single global width. Diagnostic analysis traces the residual gap in the highest-strength quartile to elevated residual variance (2.7x the pooled Q1-Q3 level) rather than a systematic bias, situating the shortfall against a proven distribution-free limit on exact conditional coverage. Marginal coverage claims for ML-based fatigue-strength predictions can conceal systematic unreliability precisely where engineering decisions are most risky; therefore, conditional coverage should be routinely assessed alongside marginal coverage.

Irene Boruah

Department of Mechanical Engineering, Dibrugarh University Institute of Engineering and Technology, Dibrugarh, 786004, Assam, India.

Conformal Prediction Materials Property Prediction Regression Prediction Intervals

Aug 4, 2026

Post-Hoc Trajectory-Risk Certification for Modular LLM-Based Security Agents

Autonomous security agents operate as staged pipelines, such as classifying network traffic and then attributing attacks to a specific technique. Split conformal prediction gives each stage finite-sample coverage, but deployment requires a trajectory-level guarantee across the full chain. These guarantees do not compose automatically when stages are independently trained and calibrated. Bonferroni allocation is distribution-free but conservative under correlated errors. We show that a natural pairwise-correlation extension to three or more stages is invalid because it gives a lower rather than an upper bound, and derive a valid spanning-tree alternative. We distinguish whether stages are dependent from whether an audit sample is large enough to certify that dependence, and give matching upper and information-theoretic lower sample-complexity bounds. We also show that coarse-to-fine label selection can create near-perfect measured correlation without learned dependence. On a two-stage intrusion-detection pipeline across 6 open LLMs and 2 datasets, removing this artifact reduces measured correlation from near 1 to 0-0.78. A direct audit of trajectory failure becomes 13.7% tighter than Bonferroni once the audit reaches the required sample size, but is worse when undersized. A modular certificate using per-stage certificates and a pairwise overlap bound yields a positive average gain of 0.6%, quantifying the cost of lacking joint access. Same-model, cross-model, and permuted-pairing tests show that residual dependence reflects shared sample difficulty, not shared model representations. Average trajectory coverage across 12 configurations is 92.7% +/- 2.4% at alpha = 0.10. Under cross-dataset deployment, single-step miscoverage reaches 100% even when accuracy remains 78%, showing that distribution shift destroys calibrated confidence before raw accuracy.

Zhenpeng Li

Guangzhou Health Science College, No. 248 Guangyuan Middle Road, Guangzhou, Guangdong 510405, China

IoT Intrusion Detection Cybersecurity Conformal Prediction LLMs for Cybersecurity LLM Agent Reliability

Aug 2, 2026

Conformalized Large Language Models under Configuration Shift

Conformal prediction (CP) is a distribution-free framework for uncertainty quantification that has recently been adapted to large language models (LLMs), providing prediction sets with finite-sample coverage guarantees under exchangeability. Yet for LLMs, nonconformity scores are often induced by an inference pipeline, not just a fixed model, making them depend not only on the data distribution but also on configurable factors such as the prompt template, decoding parameters, and deployment setting. Since such configurations are routinely modified in practice but rarely treated as a source of shift, their impact on CP validity remains poorly understood. We call this configuration shift and study it systematically along three axes: prompt template, decoding temperature, and weight quantization. In a broad empirical study spanning

9

LLMs,

4

datasets, and

4

nonconformity scores, we find that configuration shift consistently erodes CP validity, often driving empirical coverage below the target. By contrast, efficiency is largely preserved: valid prediction sets remain close in size to the i.i.d. baseline. We derive coverage lower bounds that attribute this loss to a discrepancy between calibration and test score distributions, and use their finite-sample plug-in versions as empirical diagnostics of shift severity. We further show that these findings lead to practical mitigations: bound-inspired recalibration is effective with limited test examples, while fragility-aware calibration ensembling recovers much of the lost coverage without test data.

Yuqicheng Zhu, Jialin Yu, Lin Li +7

University of Stuttgart · Robert Bosch GmbH · University of Oxford +4

Conformal Prediction Language Model Calibration LLM Uncertainty Estimation

Jul 31, 2026

Who Wins Where? Conformal Model Comparison for Local Superiority

Standard model comparison is global, aggregating losses across the covariate space to declare a single winner. This can obscure heterogeneous performance, where different models are preferable in different regions. We introduce conformalized local model comparison, a split-sample framework for constructing calibrated local best-model maps. Given a model comparison score, such as the difference between two squared losses, the method uses three disjoint splits to fit competing models, estimate local centers and scales from out-of-sample scores, and conformally calibrate residual uncertainty. At a target point, the procedure declares a local winner only when a one-sided conformal bound excludes a tie, with the score's sign determining the favored model. We prove finite-sample marginal control for one-sided erroneous declarations on the realized future comparison score, establish pointwise consistency of the localized mean-score estimator away from tie boundaries, show that aggregate comparison can disagree sharply with the prevalence of local superiority, and derive a squared-loss bias--variance decomposition that clarifies how model structure affects local wins. Synthetic and real-data experiments show that the method recovers heterogeneous winner regions, abstains under uncertainty, and yields higher conditional gain than global selection.

Yi Zhou, Baishi Li, Xuan Yao +1

Asian Institute of Digital Finance, National University of Singapore

Model Selection Selective Prediction Conformal Prediction Statistical Learning Theory

Jul 30, 2026

Mitigating Class-Tail Undercoverage in Medical Vision-Language Models under Clinical Shift

Medical vision-language models (VLMs) can retain high observed marginal coverage after clinical shift while substantially under-covering an individual disease class. The affected class varies with acquisition protocol and backbone geometry, so source prevalence does not reliably reveal the failure. Existing localized and tail-aware conformal methods respectively adapt to test neighborhoods and source-frequency tails, leaving held-out class-wise coverage failure unmodeled. We introduce Class-Tail Adaptive Localized Conformal Deferral (CALCoDe), a post-hoc reliability layer for frozen medical VLMs. Cross-fitted validation predictions identify classes at risk of undercoverage, and a disjoint calibration split estimates their class-conditional tail thresholds. CALCoDe combines each protected threshold with a localized conformal threshold using a one-sided maximum. The resulting set contains every label admitted by the localized rule, with additional protection confined to validation-identified classes. An independently calibrated support audit defers cases with insufficient inlier support. Under exchangeability among accepted examples within each protected class, CALCoDe provides finite-sample coverage at the prespecified guard level and contains the corresponding localized conformal sets; coverage on shifted external cohorts is evaluated empirically. Among standard conformal baselines and recent VLM-specific conformal methods evaluated across two dermatology shifts (HAM10000 to ISIC 2019 and HAM10000 to PAD-UFES-20) and four frozen VLM backbones (BiomedCLIP, OpenAI CLIP ViT-B/32, PubMedCLIP ViT-B/32, and MedSigLIP-448), CALCoDe is the only approach whose observed marginal and worst-class accepted coverage both reach 0.95 in all eight settings. On HAM10000 to ISIC 2019, its average worst-class accepted coverage is 0.970, compared with 0.926 for sTACP and 0.864 for LCP-VLM.

Mushir Akhtar, M. Tanveer

Department of Mathematics, Indian Institute of Technology Indore, India

Group-Conditional Conformal Prediction Conformal Prediction Medical VLMs VLM Calibration

Jul 29, 2026

Cost-Sensitive Conformal Prediction and Human-in-the-Loop Abstention for Imbalanced High-Stakes Decision Support: A Multi-Domain Benchmark

High-stakes decision systems in credit scoring, fraud detection, healthcare, and industrial safety require reliable uncertainty quantification under severe class imbalance and asymmetric error costs. Standard marginal conformal prediction (CP) provides valid overall coverage guarantees; however, we show that it severely under-covers rare, costly minority classes, with minority-class coverage dropping to as low as 0.5% on certain datasets. To characterize and address this limitation, we conduct a comprehensive benchmark comparing marginal CP, class-conditional (Mondrian) CP, and cost-controlled abstention mechanisms across 15 real-world imbalanced tabular datasets, 7 classification models, 3 probability calibration techniques, and 10 random seeds, resulting in 3,150 experimental runs. Our results show that Mondrian CP restores valid minority-class coverage, achieving an average minority-coverage improvement of 61.7 percentage points over marginal CP (p < 1e-80). Furthermore, combining Mondrian CP with cost-controlled abstention significantly reduces expected decision cost compared with standard decision boundaries, confidence-based rejectors, and risk-controlled rejectors under realistic human review budgets. We further quantify dataset-specific break-even thresholds at which deferring ambiguous instances to human experts becomes cost-effective. These findings provide practical guidance for deploying distribution-free, cost-aware uncertainty quantification in high-stakes decision support systems.

Manpreet Singh, Akshatha Srikantha, Shyamal Lakhanpal

Class-Imbalanced Learning Cost-Sensitive Learning Selective Prediction Conformal Prediction

Jul 29, 2026

Simultaneous Coverage and Efficiency Guarantee in Online Conformal Prediction

Adaptive conformal inference (ACI) of Gibbs and Cand{è}s and its variants are the standard approach to online conformal prediction under distribution shift, but they suffer from three fundamental limitations. First, their guarantees control only the signed long-run coverage error: persistent miscoverage in one direction can be masked by compensating errors later, so a method can satisfy the theoretical guarantee while being badly wrong for extended periods. Second, existing guarantees say nothing about prediction-set size, so validity can be achieved trivially at the cost of unduly wide prediction sets. Third, the efficiency guarantees that do exist compare against a fixed predictor chosen in hindsight, a benchmark that becomes increasingly less meaningful once the data-generating distribution shifts, since the very notion of an optimal threshold then changes over time. We consider a unified online learning framework that simultaneously controls absolute, non-cancelling coverage violation and prediction-set efficiency against a dynamically evolving benchmark for three important models. In the fully adversarial setting, exploiting the fact that the standard ACI update is exactly projected online gradient descent on the pinball loss, we derive simultaneous coverage and efficiency guarantees for arbitrary monotone Lipschitz efficiency objectives, with no distributional or {\it convexity} assumptions. In the stochastic setting with full-score feedback, we propose a sliding-window quantile tracker and establish a matching minimax lower bound showing our algorithm is rate-optimal. In the covariate-dependent stochastic setting, we develop a partitioned ACI algorithm that tracks a function-valued oracle threshold, and derive simultaneous coverage and efficiency guarantees.

Rahul Vaze

Tata Institute of Fundamental Research, Mumbai

Set Prediction Conformal Prediction Adaptive Conformal Inference Statistical Learning Theory

Jul 29, 2026

Conformal Changepoint Localization and Root Cause Analysis with Corrupted Observations

Detecting when the statistical behavior of an engineered system changes, and identifying which component is responsible, are core problems in the monitoring of telecommunication networks, robotic platforms, security infrastructure, and multi-agent systems. In safety- and mission-critical deployments, such decisions must be accompanied by statistical reliability guarantees rather than by point estimates alone. Conformal changepoint localization (CONCH) and conformal root cause analysis (CROC) meet this need by returning confidence sets that contain the true changepoint, or the true root-cause stream, with a user-specified probability, without parametric assumptions on the data-generating process. In practice, however, observations are frequently corrupted, e.g., by outliers, sensor faults, or adversarial perturbations. While the finite-sample coverage of these procedures is preserved under contamination, the resulting confidence sets can become uninformatively large. Adopting a Huber-type contamination model, this paper proposes weighted CONCH (W-CONCH) and weighted CROC (W-CROC), which downweight observations that are likely to be corrupted with the goal of reducing confidence set size when data may be corrupted. The weighting mechanism, derived from a formal bound on the unknown corrupted data densities, leverages pre-existing second-order classifier-based uncertainty signals, such as those produced by evidential deep learning or Bayesian learning. W-CONCH and W-CROC are further generalized by introducing a meta-learning procedure for the weights that optimizes a differentiable surrogate of the confidence set size. Experiments on image-based and real-world changepoint and root-cause benchmarks show that uncertainty-based weighting substantially reduces confidence set size while maintaining the target coverage.

Seunghun Yu, Meiyi Zhu, Petar Popovski +2

Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea · Department of Engineering, King’s College London, WC2R 2LS, London, U.K. · Department of Electronic Systems, Aalborg University, 9220 Aalborg, Denmark +2

Conformal Prediction Change-Point Detection Data Contamination Root Cause Analysis

Jul 28, 2026

HeAD-CP: Heterophily-Aware Diffused Conformal Prediction Sets for Graph Neural Networks

Conformal prediction (CP) provides distribution-free uncertainty quantification, and its extension to graphs is an active research direction. Diffused Adaptive Prediction Sets (DAPS) is a widely used graph-aware diffusion baseline, propagating Adaptive Prediction Sets (APS) non-conformity scores along edges with a uniform coefficient

λ

. We identify a fundamental shortcoming of this design: the uniform low-pass diffusion presupposes graph homophily and proves detrimental on heterophilic graphs, enlarging the mean prediction-set size by up to 10.6% relative to plain APS. To mitigate this, we propose HeAD-CP, a family of node-wise diffusion variants whose coefficients are determined by a label-free local-homophily estimate derived from the GNN softmax. Three variants, namely signed-

γ

, edge-compatibility, and a DAPS-baseline-with-correction, are most effective at extreme heterophily, intermediate heterophily, and moderate-to-high homophily, respectively, and all preserve the marginal coverage guarantee. On ten benchmarks, the HeAD-CP family stays at or below plain APS on every dataset, while DAPS exceeds APS on six. The post-hoc oracle over the family improves over DAPS on 8/10 datasets at

p<0.01

(paired Wilcoxon), with the largest gains on heterophilic graphs (10.3% on Texas); on the two homophilic datasets where DAPS still wins (CiteSeer, PubMed), it retains a marginal advantage of at most 0.002, statistically insignificant on CiteSeer (

p=0.23

). Designing a calibrated label-free selector that approaches this oracle is the main outstanding empirical question.

Phan Binh Nguyen Lam, Nguyen Thai Anh

Faculty of Information Technology, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam · Faculty of Information Technology, Van Lang School of Technology, Van Lang University, Ho Chi Minh City, Vietnam

Graph Neural Networks Conformal Prediction Graph Heterophily Graph Diffusion