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As machine learning (ML) models are increasingly deployed in high-stakes domains, trustworthy uncertainty quantification (UQ) is critical for ensuring the safety and reliability of these models. Traditional UQ methods rely on specifying a…

Machine Learning · Statistics 2025-05-14 Abhineet Agarwal , Michael Xiao , Rebecca Barter , Omer Ronen , Boyu Fan , Bin Yu

Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…

In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we…

Machine Learning · Computer Science 2024-02-26 Christian Moya , Amirhossein Mollaali , Zecheng Zhang , Lu Lu , Guang Lin

Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating…

Machine Learning · Statistics 2024-05-30 Charles Guille-Escuret , Eugene Ndiaye

Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial…

Machine Learning · Statistics 2024-10-29 Alberto Portela , Julio R. Banga , Marcos Matabuena

We introduce Conformal Interquantile Regression (CIR), a conformal regression method that efficiently constructs near-minimal prediction intervals with guaranteed coverage. CIR leverages black-box machine learning models to estimate outcome…

Machine Learning · Statistics 2026-01-07 Naixin Guo , Rui Luo , Zhixin Zhou

Conformal Prediction provides distribution-free prediction intervals with guaranteed coverage, but its reliance on a single global calibration threshold obscures the sources of uncertainty at the instance level. In particular, it conflates…

Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable…

Machine Learning · Computer Science 2020-05-21 Lior Hirschfeld , Kyle Swanson , Kevin Yang , Regina Barzilay , Connor W. Coley

Conformalized quantile regression is a procedure that inherits the advantages of conformal prediction and quantile regression. That is, we use quantile regression to estimate the true conditional quantile and then apply a conformal step on…

Machine Learning · Statistics 2023-11-02 Martim Sousa , Ana Maria Tomé , José Moreira

Among the many ways of quantifying uncertainty in a regression setting, specifying the full quantile function is attractive, as quantiles are amenable to interpretation and evaluation. A model that predicts the true conditional quantiles…

Machine Learning · Computer Science 2021-12-10 Youngseog Chung , Willie Neiswanger , Ian Char , Jeff Schneider

Quantile Regression (QR) provides a way to approximate a single conditional quantile. To have a more informative description of the conditional distribution, QR can be merged with deep learning techniques to simultaneously estimate multiple…

Machine Learning · Computer Science 2022-02-01 Axel Brando , Joan Gimeno , Jose A. Rodríguez-Serrano , Jordi Vitrià

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in…

Machine Learning · Statistics 2025-07-02 Sunay Joshi , Shayan Kiyani , George Pappas , Edgar Dobriban , Hamed Hassani

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…

Machine Learning · Computer Science 2023-06-21 Xing Yan , Yonghua Su , Wenxuan Ma

Reliable uncertainty quantification is crucial for reinforcement learning (RL) in high-stakes settings. We propose a unified conformal prediction framework for infinite-horizon policy evaluation that constructs distribution-free prediction…

Machine Learning · Statistics 2025-10-31 Feichen Gan , Youcun Lu , Yingying Zhang , Yukun Liu

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…

Machine Learning · Statistics 2023-06-06 Margaux Zaffran , Aymeric Dieuleveut , Julie Josse , Yaniv Romano

This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches--such as directional quantiles,…

Econometrics · Economics 2026-01-01 Antonio F. Galvao , Gabriel Montes-Rojas

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in…

Machine Learning · Computer Science 2025-04-22 Amirhossein Mollaali , Christian Bolivar Moya , Amanda A. Howard , Alexander Heinlein , Panos Stinis , Guang Lin

We introduce a fine-grained framework for uncertainty quantification of predictive models under distributional shifts. This framework distinguishes the shift in covariate distributions from that in the conditional relationship between the…

Methodology · Statistics 2025-05-20 Jiahao Ai , Zhimei Ren

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…

Machine Learning · Statistics 2026-03-30 Gabriel Melo , Thibaut de Saivre , Anna Calissano , Florence d'Alché-Buc

The quantification of uncertainty in prediction models is crucial for reliable decision-making, yet remains a significant challenge. Interval time series forecasting offers a principled solution to this problem by providing prediction…

Machine Learning · Computer Science 2026-04-20 Miaoxuan Zhu , Yi Yu , Yuyang Li , Wei Li , Guangcan Liu