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.

Apr 13, 2026

Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables

Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discovery rate (FDR). Existing methods fix the target FDR level before observing data, which prevents the user from adapting the balance between number of selected test inputs and FDR to downstream needs and constraints based on the available data. For example, in genomics or neuroimaging, researchers often inspect the distribution of test statistics, and decide how aggressively to pursue candidates based on observed evidence strength and available follow-up resources. To address this limitation, we introduce post-hoc CS (PH-CS), which generates a path of candidate selection sets, each paired with a data-driven false discovery proportion (FDP) estimate. PH-CS lets the user select any operating point on this path by maximizing a user-specified utility, arbitrarily balancing selection size and FDR. Building on conformal e-variables and the e-Benjamini-Hochberg (e-BH) procedure, PH-CS is proved to provide a finite-sample post-hoc reliability guarantee whereby the ratio between estimated FDP level and true FDP is, on average, upper bounded by 1, so that the average estimated FDP is, to first order, a valid upper bound on the true FDR. PH-CS is extended to control quality defined in terms of a general risk. Experiments on synthetic and real-world datasets demonstrate that, unlike CS, PH-CS can consistently satisfy user-imposed utility constraints while producing reliable FDP estimates and maintaining competitive FDR control.

Meiyi Zhu, Osvaldo Simeone

Department of Engineering, King’s College London, WC2R 2LS, London, U.K. · Institute for Intelligent Networked Systems, Northeastern University London, E1 8PH London, U.K.

FDR Control E-Values Conformal Prediction

Apr 10, 2026

Uncertainty-Aware Transformers: Conformal Prediction for Language Models

Transformers have had a profound impact on the field of artificial intelligence, especially on large language models and their variants. However, as was the case with neural networks, their black-box nature limits trust and deployment in high-stakes settings. For models to be genuinely useful and trustworthy in critical applications, they must provide more than just predictions: they must supply users with a clear understanding of the reasoning that underpins their decisions. This article presents an uncertainty quantification framework for transformer-based language models. This framework, called CONFIDE (CONformal prediction for FIne-tuned DEep language models), applies conformal prediction to the internal embeddings of encoder-only architectures, like BERT and RoBERTa, while enabling hyperparameter tuning. CONFIDE uses either [CLS] token embeddings or flattened hidden states to construct class-conditional nonconformity scores, enabling statistically valid prediction sets with instance-level explanations. Empirically, CONFIDE improves test accuracy by up to 4.09% on BERT-tiny and achieves greater correct efficiency (i.e., the expected size of the prediction set conditioned on it containing the true label) compared to prior methods, including NM2 and VanillaNN. We show that early and intermediate transformer layers often yield better-calibrated and more semantically meaningful representations for conformal prediction. In resource-constrained models and high-stakes tasks with ambiguous labels, CONFIDE offers robustness and interpretability where softmax-based uncertainty fails. We position CONFIDE as a framework for practical diagnostic and efficiency/robustness improvement over prior conformal baselines.

Abhiram Vellore, Niraj K. Jha

Department of Electrical and Computer Engineering, Princeton University

LLM Uncertainty Estimation Conformal Prediction Language Model Calibration

Apr 9, 2026

From Debate to Decision: Conformal Social Choice for Safe Multi-Agent Deliberation

Multi-agent debate improves LLM reasoning, yet agreement among agents is not evidence of correctness. When agents converge on a wrong answer through social reinforcement, consensus-based stopping commits that error to an automated action with no recourse. We introduce Conformal Social Choice, a post-hoc decision layer that converts debate outputs into calibrated act-versus-escalate decisions. Verbalized probability distributions from heterogeneous agents are aggregated via a linear opinion pool and calibrated with split conformal prediction, yielding prediction sets with a marginal coverage guarantee: the correct answer is included with probability

{\geq}\,1{-}α

, without assumptions on individual model calibration. A hierarchical action policy maps singleton sets to autonomous action and larger sets to human escalation. On eight MMLU-Pro domains with three agents (Claude Haiku, DeepSeek-R1, Qwen-3 32B), coverage stays within 1--2 points of the target. The key finding is not that debate becomes more accurate, but that the conformal layer makes its failures actionable: 81.9% of wrong-consensus cases are intercepted at

α{=}0.05

. Because the layer refuses to act on cases where debate is confidently wrong, the remaining conformal singletons reach 90.0--96.8% accuracy (up to 22.1pp above consensus stopping) -- a selection effect, not a reasoning improvement. This safety comes at the cost of automation, but the operating point is user-adjustable via

α

.

Mengdie Flora Wang, Haochen Xie, Guanghui Wang +9

AWS Generative AI Innovation Center · HSBC Holdings Plc., HSBC Technology Center, China

LLM Agent Safety Selective Prediction Conformal Prediction Multi-Agent Debate Multi-Agent Consensus

Apr 7, 2026

Weighted Bayesian Conformal Prediction

Machine learning predictors are rarely deployed on data that match the data they were calibrated on. Conformal prediction and its risk-control generalization promise distribution-free guarantees at deployment, but only under exchangeability or a covariate shift whose likelihood ratio is known exactly -- and the estimated-ratio case, the one that occurs in practice, is explicitly open, out of reach of the Bayesian construction available under exchangeability. We reach it from a different starting point: pushing a Dirichlet process prior on the calibration distribution through the likelihood ratio yields the exact Bayesian posterior over the deployed risk. That posterior is exact given the weight function, which at deployment is itself estimated, so we further prove finite-sample upper and lower bounds on the risk the selected threshold actually incurs, in terms of the weight-estimation error and the conditional shift. On synthetic and real covariate shifts, in regression and classification, the realized failure rate then stays close to target where shift-blind selection fails, and what deployment receives is a posterior over the risk of every threshold rather than a single number.

Xiayin Lou, Peng Luo

Technical University of Munich · Massachusetts Institute of Technology

Conformal Prediction Weighted Conformal Prediction Conformal Risk Control Distribution Shift Robustness

Apr 7, 2026

Staggered Integral Online Conformal Prediction for Safe Dynamics Adaptation with Multi-Step Coverage Guarantees

Safety-critical control of uncertain, adaptive systems often relies on conservative, worst-case uncertainty bounds that limit closed-loop performance. Online conformal prediction is a powerful data-driven method for quantifying uncertainty when truth values of predicted outputs are revealed online; however, for systems that adapt the dynamics without measurements of the state derivatives, standard online conformal prediction is insufficient to quantify the model uncertainty. We propose Staggered Integral Online Conformal Prediction (SI-OCP), an algorithm utilizing an integral score function to quantify the lumped effect of disturbance and learning error. This approach provides long-run coverage guarantees, resulting in long-run safety when synthesized with safety-critical controllers, including robust tube model predictive control. Finally, we validate the proposed approach through a numerical simulation of an all-layer deep neural network (DNN) adaptive quadcopter using robust tube (MPC), highlighting the applicability of our method to complex learning parameterizations and control strategies.

Daniel M. Cherenson, Dimitra Panagou

Robotics Department, University of Michigan, Ann Arbor, MI, USA

Conformal Prediction Adaptive Conformal Inference Safety-Critical Control

Apr 4, 2026

Debiased Machine Learning for Conformal Prediction of Counterfactual Outcomes Under Runtime Confounding

Data-driven decision making frequently relies on predicting counterfactual outcomes. In practice, researchers commonly train counterfactual prediction models on a source dataset to inform decisions on a possibly separate target population. Conformal prediction has arisen as a popular method for producing assumption-lean prediction intervals for counterfactual outcomes that would arise under different treatment decisions in the target population of interest. However, existing methods require that every confounding factor of the treatment-outcome relationship used for training on the source data is additionally measured in the target population, risking miscoverage if important confounders are unmeasured in the target population. In this paper, we introduce a computationally efficient debiased machine learning framework that allows for valid prediction intervals when only a subset of confounders is measured in the target population, a common challenge referred to as runtime confounding. Grounded in semiparametric efficiency theory, we show the resulting prediction intervals achieve desired coverage rates with faster convergence compared to standard methods. Through numerous synthetic and semi-synthetic experiments, we demonstrate the utility of our proposed method.

Keith Barnatchez, Kevin P. Josey, Rachel C. Nethery +1

Department of Biostatistics, Harvard T.H. Chan School of Public Health · Department of Biostatistics and Informatics, Colorado School of Public Health · Department of Data Science, Dana Farber Cancer Institute

Counterfactual Prediction Conformal Prediction Debiased ML

Apr 1, 2026

Adaptive Stopping for Multi-Turn LLM Reasoning

Large Language Models (LLMs) increasingly rely on multi-turn reasoning and interaction, such as adaptive retrieval-augmented generation (RAG) and ReAct-style agents, to answer difficult questions. These methods improve accuracy by iteratively retrieving information, reasoning, or acting, but introduce a key challenge: When should the model stop? Existing approaches rely on heuristic stopping rules or fixed turn budgets and provide no formal guarantees that the final prediction still contains the correct answer. This limitation is particularly problematic in high-stakes domains such as finance and healthcare, where unnecessary turns increase cost and latency, while stopping too early risks incorrect decisions. Conformal prediction (CP) provides formal coverage guarantees, but existing LLM-CP methods only apply to a single model output and cannot handle multi-turn pipelines with adaptive stopping. To address this gap, we propose Multi-Turn Language Models with Conformal Prediction (MiCP), the first CP framework for multi-turn reasoning. MiCP allocates different error budgets across turns, enabling the model to stop early while maintaining an overall coverage guarantee. We demonstrate MiCP on adaptive RAG and ReAct, where it achieves the target coverage on both single-hop and multi-hop question answering benchmarks while reducing the number of turns, inference cost, and prediction set size. We further introduce a new metric that jointly evaluates coverage validity and answering efficiency.

Xiaofan Zhou, Huy Nguyen, Bo Yu +2

Department of Computer Science, University of Illinois Chicago, Chicago, IL 60607, USA · Data science, Augustana College, Rock Island, IL 61201, USA · Department of Civil and Environmental Engineering, University of Utah, Salt Lake City, UT 84112, USA

Efficient Language Model Reasoning Conformal Prediction

Apr 1, 2026

Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoning

While test-time scaling has enabled large language models to solve highly difficult tasks, state-of-the-art results come at exorbitant compute costs. These inefficiencies can be attributed to the miscalibration of post-trained language models, and the lack of calibration in popular sampling techniques. Here, we present Online Reasoning Calibration (ORCA), a framework for calibrating the sampling process that draws upon conformal prediction and test-time training. Specifically, we introduce a meta-learning procedure that updates the calibration module for each input. This allows us to provide valid confidence estimates under distributional shift, e.g. in thought patterns that occur across different stages of reasoning, or in prompt distributions between model development and deployment. ORCA not only provides theoretical guarantees on conformal risks, but also empirically shows higher efficiency and generalization across different reasoning tasks. At risk level

δ=0.1

, ORCA improves Qwen2.5-32B efficiency on in-distribution tasks with savings up to 47.5% with supervised labels and 40.7% with self-consistency labels. Under zero-shot out-of-domain settings, it improves MATH-500 savings from 24.8% of the static calibration baseline to 67.0% while maintaining a low empirical error rate, and the same trend holds across model families and downstream benchmarks. Our code is publicly available at https://github.com/wzekai99/ORCA.

Cai Zhou, Zekai Wang, Menghua Wu +6

Department of Electrical Engineering and Computer Science (MIT EECS) · Computer Science and Artificial Intelligence Laboratory (MIT CSAIL) · Laboratory for Information and Decision Systems (MIT LIDS) +1

Language Model Calibration Confidence Estimation in Language Models Efficient Language Model Reasoning Conformal Prediction Test-Time Training

Mar 28, 2026

Conformal Prediction Assessment: A Framework for Conditional Coverage Evaluation and Selection

Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing conditional validity is challenging, as standard stratification methods suffer from the curse of dimensionality. We propose Conformal Prediction Assessment (CPA), a framework that reframes the evaluation of conditional coverage as a supervised learning task by training a reliability estimator that predicts instance-level coverage probabilities. Building on this estimator, we introduce the Conditional Validity Index (CVI), which decomposes reliability into safety (undercoverage risk) and efficiency (overcoverage cost). We establish convergence rates for the reliability estimator and prove the consistency of CVI-based model selection. Extensive experiments on synthetic and real-world datasets demonstrate that CPA effectively diagnoses local failure modes and that CC-Select, our CVI-based model selection algorithm, consistently identifies predictors with superior conditional coverage performance.

Zheng Zhou, Xiangfei Zhang, Chongguang Tao +1

Qiuzhen College, Tsinghua University · Yau Mathematical Sciences Center, Tsinghua University

Conformal Prediction

Mar 28, 2026

Conformalized Signal Temporal Logic Inference under Covariate Shift

Signal Temporal Logic (STL) inference learns interpretable logical rules for temporal behaviors in dynamical systems. To ensure the correctness of learned STL formulas, recent approaches have incorporated conformal prediction as a statistical tool for uncertainty quantification. However, most existing methods rely on the assumption that calibration and testing data are identically distributed and exchangeable, an assumption that is frequently violated in real-world settings. This paper proposes a conformalized STL inference framework that explicitly addresses covariate shift between training and deployment trajectories dataset. From a technical standpoint, the approach first employs a template-free, differentiable STL inference method to learn an initial model, and subsequently refines it using a limited deployment side dataset to promote distribution alignment. To provide validity guarantees under distribution shift, the framework estimates the likelihood ratio between training and deployment distributions and integrates it into an STL-robustness-based weighted conformal prediction scheme. Experimental results on trajectory datasets demonstrate that the proposed framework preserves the interpretability of STL formulas while significantly improving symbolic learning reliability at deployment time.

Yixuan Wang, Danyang Li, Matthew Cleaveland +2

Mingyu Cai and Yixuan Wang are with Mechanical Engineering, University of California, Riverside, CA, 92521, USA. · Danyang Li and Roberto Tron are with Mechanical Engineering, Boston University. · Matthew Cleaveland is with MIT Lincoln Laboratory, Lexington, MA, 02421, USA

Signal Temporal Logic Conformal Prediction Covariate Shift Weighted Conformal Prediction

Mar 27, 2026

Contrastive Conformal Sets

Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack a principled construction of geometric sets in the semantic feature space with distribution-free guarantees at any user-specified coverage level. We extend conformal prediction to this setting by introducing covering sets equipped with learnable generalized hyper-ball constraints. We propose a method that constructs conformal sets guaranteeing user-specified coverage of positive samples while maximizing negative sample exclusion. We theoretically motivate volume minimization as a proxy for negative exclusion, enabling our approach to operate effectively even when negative pairs are unavailable. The positive inclusion guarantee inherits the distribution-free coverage property of conformal prediction, while negative exclusion is maximized through learned set geometry optimized on a held-out training split. Experiments on simulated and real-world image datasets demonstrate improved inclusion-exclusion trade-offs compared to standard distance-based conformal baselines.

Yahya Alkhatib, Wee Peng Tay

School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore

Contrastive Learning Conformal Prediction

Mar 26, 2026

Conformal Prediction for Nonparametric Instrumental Regression

We propose a method for constructing distribution-free prediction intervals in nonparametric instrumental variable regression (NPIV), with finite-sample coverage guarantees. Building on the conditional guarantee framework in conformal inference, we reformulate conditional coverage as marginal coverage over a class of IV shifts

\mathcal{F}

. Our method can be combined with any NPIV estimator, including sieve 2SLS and other machine-learning-based NPIV methods such as neural networks minimax approaches. Our theoretical analysis establishes distribution-free, finite-sample coverage over a practitioner-chosen class of IV shifts.

Masahiro Kato

The University of Tokyo

Regression Prediction Intervals Conformal Prediction Instrumental Variable Estimation

Mar 25, 2026

Conformal Selective Prediction with General Risk Control

In deploying artificial intelligence (AI) models, selective prediction offers the option to abstain from making a prediction when uncertain about model quality. To fulfill its promise, it is crucial to enforce strict and precise error control over cases where the model is trusted. We propose Selective Conformal Risk control with E-values (SCoRE), a new framework for deriving such decisions for any trained model and any user-defined, bounded and continuously-valued risk. SCoRE offers two types of guarantees on the risk among ``positive'' cases in which the system opts to trust the model. Built upon conformal inference and hypothesis testing ideas, SCoRE first constructs a class of (generalized) e-values, which are non-negative random variables whose product with the unknown risk has expectation no greater than one. Such a property is ensured by data exchangeability without requiring any modeling assumptions. Passing these e-values on to hypothesis testing procedures, we yield the binary trust decisions with finite-sample error control. SCoRE avoids the need of uniform concentration, and can be readily extended to settings with distribution shifts. We evaluate the proposed methods with simulations and demonstrate their efficacy through applications to error management in drug discovery, health risk prediction, and large language models.

Tian Bai, Ying Jin

Department of Statistics, Stanford University · Department of Statistics and Data Science, University of Pennsylvania

Selective Prediction Conformal Risk Control Conformal Prediction E-Values

Mar 24, 2026

Conformal Cross-Modal Active Learning

Foundation models for vision have transformed visual recognition with powerful pretrained representations and strong zero-shot capabilities, yet their potential for data-efficient learning remains largely untapped. Active Learning (AL) aims to minimize annotation costs by strategically selecting the most informative samples for labeling, but existing methods largely overlook the rich multimodal knowledge embedded in modern vision-language models (VLMs). We introduce Conformal Cross-Modal Acquisition (CCMA), a novel AL framework that bridges vision and language modalities through a teacher-student architecture. CCMA employs a pretrained VLM as a teacher to provide semantically grounded uncertainty estimates, conformally calibrated to guide sample selection for a vision-only student model. By integrating multimodal conformal scoring with diversity-aware selection strategies, CCMA achieves superior data efficiency across multiple benchmarks. Our approach consistently outperforms state-of-the-art AL baselines, demonstrating clear advantages over methods relying solely on uncertainty or diversity metrics.

Huy Hoang Nguyen, Cédric Jung, Shirin Salehi +3

AIT Austrian Institute of Technology · Automation & Control Institute, Technical University of Vienna · Chair of Information Theory and Data Analytics (INDA), RWTH Aachen University

Active Learning Conformal Prediction

Mar 23, 2026

CRPS-Optimal Binning for Univariate Conformal Regression

We propose a method for non-parametric conditional distribution estimation based on partitioning covariate-sorted observations into contiguous bins and using the within-bin empirical CDF as the predictive distribution. Bin boundaries are chosen to minimise the total leave-one-out Continuous Ranked Probability Score (LOO-CRPS), which admits a closed-form cost function with

O(n^2 \log n)

precomputation and

O(n^2)

storage; the globally optimal

K

-partition is recovered by a dynamic programme in

O(n^2 K)

time. Minimisation of within-sample LOO-CRPS turns out to be inappropriate for selecting

K

as it results in in-sample optimism. We instead select

K

by

K

-fold cross-validation of test CRPS, which yields a U-shaped criterion with a well-defined minimum. Having selected

K^*

and fitted the full-data partition, we form two complementary predictive objects: the Venn prediction band and a conformal prediction set based on CRPS as the nonconformity score, which carries a finite-sample marginal coverage guarantee at any prescribed level

\varepsilon

. The conformal prediction is transductive and data-efficient, as all observations are used for both partitioning and p-value calculation, with no need to reserve a hold-out set. On real benchmarks against split-conformal competitors (Gaussian split conformal, CQR, CQR-QRF, and conformalized isotonic distributional regression), the method produces substantially narrower prediction intervals while maintaining near-nominal coverage.

Paolo Toccaceli

Centre for Reliable Machine Learning, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

Conditional Distribution Estimation Regression Prediction Intervals Conformal Prediction

Mar 23, 2026

TrustFed: Enabling Trustworthy Medical AI under Data Privacy Constraints

Protecting patient privacy remains a fundamental barrier to scaling machine learning across healthcare institutions, where centralizing sensitive data is often infeasible due to ethical, legal, and regulatory constraints. Federated learning offers a promising alternative by enabling privacy-preserving, multi-institutional training without sharing raw patient data; however, real-world deployments face severe challenges from data heterogeneity, site-specific biases, and class imbalance, which degrade predictive reliability and render existing uncertainty quantification methods ineffective. Here, we present TrustFed, a federated uncertainty quantification framework that provides distribution-free, finite-sample coverage guarantees under heterogeneous and imbalanced healthcare data, without requiring centralized access. TrustFed introduces a representation-aware client assignment mechanism that leverages internal model representations to enable effective calibration across institutions, along with a soft-nearest threshold aggregation strategy that mitigates assignment uncertainty while producing compact and reliable prediction sets. Using over 430,000 medical images across six clinically distinct imaging modalities, we conduct one of the most comprehensive evaluations of uncertainty-aware federated learning in medical imaging, demonstrating robust coverage guarantees across datasets with diverse class cardinalities and imbalance regimes. By validating TrustFed at this scale and breadth, our study advances uncertainty-aware federated learning from proof-of-concept toward clinically meaningful, modality-agnostic deployment, positioning statistically guaranteed uncertainty as a core requirement for next-generation healthcare AI systems.

Vagish Kumar, Syed Bahauddin Alam, Souvik Chakraborty

Department of Applied Mechanics Indian Institute of Technology Delhi · Grainger College of Engineering Nuclear, Plasma & Radiological Engineering Department National Center for Supercomputing Applications, Urbana, IL, USA · Department of Applied Mechanics Yardi School of Artificial Intelligence (ScAI) Grainger College of Engineering Indian Institute of Technology Delhi University of Illinois Urbana-Champaign, Urbana, IL, USA

Federated Learning Uncertainty Quantification Heterogeneous Federated Learning Conformal Prediction Medical Imaging

Mar 19, 2026

Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation

Scenario optimization and conformal prediction share a common goal, that is, turning finite samples into safety margins. Yet, different terminology often obscures the connection between their respective guarantees. This paper revisits that connection directly from a systems-and-control viewpoint. Building on the recent conformal/scenario bridge of \citet{OSullivanRomaoMargellos2026}, we extend the forward direction to feasible sample-and-discard scenario algorithms. Specifically, if the final decision is determined by a stable subset of the retained sampled constraints, the classical mean violation law admits a direct exchangeability-based derivation. In this view, discarded samples naturally appear as admissible exceptions. We also introduce a simple modular composition rule that combines several blockwise calibration certificates into a single joint guarantee. This rule proves particularly useful in multi-output prediction and finite-horizon control, where engineers must distribute risk across coordinates, constraints, or prediction steps. Finally, we provide numerical illustrations using a calibrated multi-step tube around an identified predictor. These examples compare alternative stage-wise risk allocations and highlight the resulting performance and safety trade-offs in a standard constraint-tightening problem.

Giuseppe C. Calafiore

Department of Electronics and Telecommunications Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Conformal Prediction Chance-Constrained Optimization

Mar 15, 2026

Efficient Federated Conformal Prediction with Group-Conditional Guarantee

Deploying trustworthy AI systems requires principled uncertainty quantification. Conformal prediction (CP) is a widely used framework for constructing prediction sets with distribution-free coverage guarantees. In many practical settings, including healthcare, finance, and mobile sensing, the calibration data required for CP are distributed across multiple clients, each with its own local data distribution. In this federated setting, data can often be partitioned into, potentially overlapping, groups, which may reflect client-specific strata or cross-cutting attributes such as demographic or semantic categories. We propose group-conditional federated conformal prediction (GC-FCP), a federated extension of conditional conformal calibration for a target mixture over prespecified groups. GC-FCP constructs mergeable, atom-stratified coresets from local calibration scores, enabling compact aggregation at the server when the number of active atoms is moderate. Experiments on synthetic and real-world datasets validate the performance of GC-FCP compared to centralized calibration baselines. The code of our work can be found at https://github.com/HaifengWen/GC-FCP.

Haifeng Wen, Osvaldo Simeone, Hong Xing

1IoT Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · Institute for Intelligent Networked Systems (INSI), Northeastern University London, London, UK · Department of ECE, The Hong Kong University of Science and Technology, HK SAR

Group-Conditional Conformal Prediction Conformal Prediction Federated Learning

Mar 11, 2026

Conformal e-prediction in the presence of confounding

This note extends conformal e-prediction to cover the case where there is observed confounding between the random object

X

and its label

Y

. We consider both the case where the observed data is IID and a case where some dependence between observations is permitted.

Vladimir Vovk, Ruodu Wang

Conformal Prediction

Mar 11, 2026

Beyond Accuracy: Reliability and Uncertainty Estimation in Convolutional Neural Networks

Deep neural networks (DNNs) have become integral to a wide range of scientific and practical applications due to their flexibility and strong predictive performance. Despite their accuracy, however, DNNs frequently exhibit poor calibration, often assigning overly confident probabilities to incorrect predictions. This limitation underscores the growing need for integrated mechanisms that provide reliable uncertainty estimation. In this article, we compare two prominent approaches for uncertainty quantification: a Bayesian approximation via Monte Carlo Dropout and the nonparametric Conformal Prediction framework. Both methods are assessed using two convolutional neural network architectures; H-CNN VGG16 and GoogLeNet, trained on the Fashion-MNIST dataset. The empirical results show that although H-CNN VGG16 attains higher predictive accuracy, it tends to exhibit pronounced overconfidence, whereas GoogLeNet yields better-calibrated uncertainty estimates. Conformal Prediction additionally demonstrates consistent validity by producing statistically guaranteed prediction sets, highlighting its practical value in high-stakes decision-making contexts. Overall, the findings emphasize the importance of evaluating model performance beyond accuracy alone and contribute to the development of more reliable and trustworthy deep learning systems.

Sanne Ruijs, Alina Kosiakova, Farrukh Javed

Department of Economics, Lund University, Sweden · Department of Statistics, Lund University, Sweden

Uncertainty Quantification Uncertainty Calibration Conformal Prediction Convolutional Neural Networks Bayesian Neural Networks

Mar 9, 2026

Formation-Aware Adaptive Conformalized Perception for Safe Leader-Follower Multi-Robot Systems

This paper considers the perception safety problem in distributed vision-based leader-follower formations, where each robot uses onboard perception to estimate relative states, track desired setpoints, and keep the leader within its camera field of view (FOV). Safety is challenging due to heteroscedastic perception errors and the coupling between formation maneuvers and visibility constraints. We propose a distributed, formation-aware adaptive conformal prediction method based on Risk-Aware Mondrian CP to produce formation-conditioned uncertainty quantiles. The resulting bounds tighten in high-risk configurations (near FOV limits) and relax in safer regions. We integrate these bounds into a Formation-Aware Conformal CBF-QP with a smooth margin to enforce visibility while maintaining feasibility and tracking performance. Gazebo simulations show improved formation success rates and tracking accuracy over non-adaptive (global) CP baselines that ignore formation-dependent visibility risk, while preserving finite-sample probabilistic safety guarantees. The experimental videos are available on the project website\footnote{Project Website: https://nail-uh.github.io/iros2026.github.io/}.

Richie R. Suganda, Bin Hu

Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004, USA. · Department of Engineering Technology, University of Houston, Houston, TX 77004, USA.

Robot Safety Multi-Robot Formation Control Conformal Prediction Robotic Perception Control Barrier Functions

Mar 8, 2026

Beyond Data Splitting: Full-Data Conformal Prediction by Differential Privacy

Privacy protection and uncertainty quantification are increasingly important in data-driven decision making. Conformal prediction provides finite-sample marginal coverage, but existing private approaches often rely on data splitting, reducing the effective sample size. We propose a full-data privacy-preserving conformal prediction framework that avoids splitting. Our framework leverages stability induced by differential privacy to control the gap between in-sample and out-of-sample conformal scores, and pairs this with a conservative private quantile routine designed to prevent under-coverage. We show that a generic differential privacy guarantee yields a universal coverage floor, yet cannot generally recover the nominal

1-α

level. We then provide a refined, mechanism-specific stability analysis and yields asymptotic recovery of the nominal level. Experiments demonstrate sharper prediction sets than the split-based private baseline.

Young Hyun Cho, Jordan Awan

Purdue University · University of Pittsburgh

Conformal Prediction Differential Privacy

Mar 6, 2026

CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression

Conformal prediction delivers prediction intervals with distribution-free coverage, but its intervals can look overconfident in regions where the model is extrapolating, because standard conformal scores do not explicitly represent epistemic uncertainty. Credal methods, by contrast, make epistemic effects visible by working with sets of plausible predictive distributions, but they are typically model-based and lack calibration guarantees. We introduce CREDO, a simple "credal-then-conformalize" recipe that combines both strengths. CREDO first builds an interpretable credal envelope that widens when local evidence is weak, then applies split conformal calibration on top of this envelope to guarantee marginal coverage without further assumptions. This separation of roles yields prediction intervals that are interpretable: their width can be decomposed into aleatoric noise, epistemic inflation, and a distribution-free calibration slack. We provide a fast implementation based on trimming extreme posterior predictive endpoints, prove validity, and show on benchmark regressions that CREDO maintains target coverage while improving sparsity adaptivity at competitive efficiency.

Luben M. C. Cabezas, Sabina J. Sloman, Bruno M. Resende +3

Department of Statistics, Federal University of S˜ao Carlos, S˜ao Carlos, Brazil · Institute of Mathematics and Computer Science , University of S˜ao Paulo, S˜ao Carlos, Brazil · Universit´e Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, France +1

Regression Prediction Intervals Conformal Prediction Epistemic Uncertainty

Mar 5, 2026

Uncertainty-Aware Solar Flare Regression

Current solar flare predictions often lack precise quantification of their reliability, resulting in frequent false alarms, particularly when dealing with datasets skewed towards extreme events. To improve the trustworthiness of space weather forecasting, it is crucial to establish confidence intervals for model predictions. Conformal prediction, a machine learning framework, presents a promising avenue for this purpose by constructing prediction intervals that ensure valid coverage in finite samples without making assumptions about the underlying data distribution. In this study, we explore the application of conformal prediction to regression tasks in space weather forecasting. Specifically, we implement full-disk solar flare prediction using images created from magnetic field maps and adapt four pre-trained deep learning models to incorporate three distinct methods for constructing confidence intervals: conformal prediction, quantile regression, and conformalized quantile regression. Our experiments demonstrate that conformalized quantile regression achieves higher coverage rates and more favorable average interval lengths compared to alternative methods, underscoring its effectiveness in enhancing the reliability of solar weather forecasting models.

Jinsu Hong, Chetraj Pandey, Berkay Aydin

Computer Science, Georgia State University, Atlanta, USA · Computer Science, Texas Christian University, Texas, USA

Regression Prediction Intervals Conformal Prediction

Mar 2, 2026

Conformal Graph Prediction with Z-Gromov-Wasserstein Distances

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal prediction framework for graph-valued outputs, providing distribution-free coverage guarantees in structured output spaces. Our method defines nonconformity via the Z-Gromov-Wasserstein distance, instantiated in practice through Fused Gromov-Wasserstein (FGW), enabling permutation invariant comparison between predicted and candidate graphs. To obtain adaptive prediction sets, we introduce Score Conformalized Quantile Regression (SCQR), an extension of Conformalized Quantile Regression (CQR) to handle complex output spaces such as graph-valued outputs. We evaluate the proposed approach on a synthetic task and a real problem of molecule identification.

Gabriel Melo, Thibaut de Saivre, Anna Calissano +1

LTCI, Télécom Paris, Intistut Polytechnique de Paris, Palaiseau, France · Department of Statistical Science, University College London, London, UK

Conformal Prediction

Mar 2, 2026

Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventions

Selective conformal prediction can yield substantially tighter uncertainty sets when we can identify calibration examples that are exchangeable with the test example. In interventional settings, such as perturbation experiments in genomics, exchangeability often holds only within subsets of interventions that leave a target variable "unaffected" (e.g., non-descendants of an intervened node in a causal graph). We study the practical regime where this invariance structure is unknown and must be estimated from data. Our main result quantifies how coverage degrades when the estimated safe calibration set accidentally includes interventions that affect the target, and gives a conservative correction when an upper bound on this error is available. Rather than learning a full causal graph, we learn only the intervention-target relationships needed to choose calibration interventions. We give algorithms for this partial learning task and evaluate them on synthetic structural equation models and Replogle K562 CRISPR-interference data, where the experiments illustrate synthetic gains from selective calibration and finite-sample tradeoffs on real perturbation screens.

Amir Asiaee, Kavey Aryan, James P. Long

Department of Biostatistics, Vanderbilt University Medical Center, TN 37203, USA · Department of Informatics, King’s College London, London, UK · Department of Biostatistics, MD Anderson Cancer Center, Houston, TX, USA

Selective Inference Causal Structure Learning Conformal Prediction Genomics Causal Intervention

Mar 2, 2026

Co-optimization for Adaptive Conformal Prediction

Conformal prediction (CP) provides finite-sample, distribution-free marginal coverage, but standard conformal regression intervals can be inefficient under heteroscedasticity and skewness. In particular, popular constructions such as conformalized quantile regression (CQR) often inherit a fixed notion of center and enforce equal-tailed errors, which can displace the interval away from high-density regions and produce unnecessarily wide sets. We propose Co-optimization for Adaptive Conformal Prediction (CoCP), a framework that learns prediction intervals by jointly optimizing a center

m(x)

and a radius

h(x)

.CoCP alternates between (i) learning

h(x)

via quantile regression on the folded absolute residual around the current center, and (ii) refining

m(x)

with a differentiable soft-coverage objective whose gradients concentrate near the current boundaries, effectively correcting mis-centering without estimating the full conditional density. Finite-sample marginal validity is guaranteed by split-conformal calibration with a normalized nonconformity score. Theory characterizes the population fixed point of the soft objective and shows that, under standard regularity conditions, CoCP asymptotically approaches the length-minimizing conditional interval at the target coverage level as the estimation error and smoothing vanish. Experiments on synthetic and real benchmarks demonstrate that CoCP yields consistently shorter intervals and achieves state-of-the-art conditional-coverage diagnostics.

Xiaoyi Su, Zhixin Zhou, Rui Luo

Department of Systems Engineering, City University of Hong Kong, Hong Kong SAR, China · Alpha Benito Research, Los Angeles, USA

Conformal Prediction Regression Prediction Intervals

Mar 1, 2026

Conformal Prediction for Risk-Controlled Medical Entity Extraction Across Clinical Domains

Large Language Models (LLMs) are increasingly used for medical entity extraction, yet their confidence scores are often miscalibrated, limiting safe deployment in clinical settings. We present a conformal prediction framework that provides finite-sample coverage guarantees for LLM-based extraction across two clinical domains. First, we extract structured entities from 1,000 FDA drug labels across eight sections using GPT-4.1, verified via FactScore-based atomic statement evaluation (97.7% accuracy over 128,906 entities). Second, we extract radiological entities from MIMIC-CXR reports using the RadGraph schema with GPT-4.1 and Llama-4-Maverick, evaluated against physician annotations (entity F1: 0.81 to 0.84). Our central finding is that miscalibration direction reverses across domains: on well-structured FDA labels, models are underconfident, requiring modest conformal thresholds (

τ\approx 0.06

), while on free-text radiology reports, models are overconfident, demanding strict thresholds (

τ

up to 0.99). Despite this heterogeneity, conformal prediction achieves target coverage (

\geq 90\%

) in both settings with manageable rejection rates (9--13%). These results demonstrate that calibration is not a global model property but depends on document structure, extraction category, and model architecture, motivating domain-specific conformal calibration for safe clinical deployment.

Manil Shrestha, Edward Kim

Department of Computer Science, Drexel University, Philadelphia, USA

Language Model Calibration Conformal Prediction Medical LLMs Clinical Information Extraction

Feb 28, 2026

Efficient Conformal Volumetry for Template-Based Segmentation

Template-based segmentation, a widely used paradigm in medical imaging, propagates anatomical labels via deformable registration from a labeled atlas to a target image, and is often used to compute volumetric biomarkers for downstream decision-making. While conformal prediction (CP) provides finite-sample valid intervals for scalar metrics, existing segmentation-based uncertainty quantification (UQ) approaches either rely on learned model features, often unavailable in classic template-based pipelines, or treat the registration process as a black box, resulting in overly conservative intervals when applied directly in output space. We introduce ConVOLT, a CP framework that achieves efficient volumetric UQ by conditioning calibration on properties of the estimated deformation field from template-based segmentation. ConVOLT calibrates a learned volumetric scaling factor from deformation space features. We evaluate ConVOLT on template-based segmentation tasks involving global, regional, and label volumetry across multiple datasets and registration methods. ConVOLT achieves target coverage while producing substantially tighter intervals than output-space conformal baselines. Our work paves way to exploit the registration process for efficient UQ in medical imaging pipelines.

Matt Y. Cheung, Ashok Veeraraghavan, Guha Balakrishnan

Department of Electrical & Computer Engineering Rice University Houston, TX 77005, USA

Segmentation Uncertainty Estimation Medical Image Analysis Conformal Prediction Medical Image Segmentation

Feb 27, 2026

Proof-of-Perception: Certified Tool-Using Multimodal Reasoning with Compositional Conformal Guarantees

We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise uncertainty; a lightweight controller uses these certificates to allocate compute under a budget, expanding with extra tool calls only when needed and stopping early otherwise. This grounds answers in verifiable evidence, reduces error compounding and hallucinations, and enables principled accuracy-compute trade-offs. Across document, chart, and multi-image QA benchmarks, PoP improves performance and reliability over strong chain-of-thought, ReAct-style, and program-of-thought baselines while using computation more efficiently.

Arya Fayyazi, Haleh Akrami

University of Southern California, Los Angeles, CA · Nuro, Mountain View, CA

Multimodal Reasoning Multimodal Tool Use Multimodal QA Efficient Multimodal Inference Conformal Prediction