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Predicting sets of outcomes -- instead of unique outcomes -- is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to…

Methodology · Statistics 2023-06-21 Hongxiang Qiu , Edgar Dobriban , Eric Tchetgen Tchetgen

In this paper, we propose a novel framework for non-stationary time-series analysis that replaces conventional correlation-based statistics with direct estimation of statistical dependence in the normalized joint density of input and target…

Machine Learning · Computer Science 2026-04-09 Yao Sun , Bo Hu , Jose Principe

Credible intervals and credible sets, such as highest posterior density (HPD) intervals, form an integral statistical tool in Bayesian phylogenetics, both for phylogenetic analyses and for development. Readily available for continuous…

Data Structures and Algorithms · Computer Science 2026-05-05 Jonathan Klawitter , Alexei J. Drummond

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

We propose Conformal Seasonal Pools (CSP), a training-free probabilistic time-series forecaster that mixes same-season empirical draws with signed residual draws around a seasonal naive forecast. In an audited rolling-origin benchmark on…

Machine Learning · Statistics 2026-05-06 Valery Manokhin

Conformal prediction provides a pivotal and flexible technique for uncertainty quantification by constructing prediction sets with a predefined coverage rate. Many online conformal prediction methods have been developed to address data…

Machine Learning · Statistics 2026-02-25 Dongjian Hu , Junxi Wu , Shu-Tao Xia , Changliang Zou

Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the…

Machine Learning · Computer Science 2014-04-09 Evgeny Burnaev , Vladimir Vovk

Conformal prediction provides distribution-free prediction sets with guaranteed marginal coverage. However, in split conformal prediction this guarantee is training-conditional only in expectation: across many calibration draws, the average…

Machine Learning · Computer Science 2025-09-22 Petrus H. Zwart

In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can…

Methodology · Statistics 2026-03-12 Han Lin Shang

Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…

Methodology · Statistics 2023-03-20 Rina Foygel Barber , Emmanuel J. Candes , Aaditya Ramdas , Ryan J. Tibshirani

A reliable representation of uncertainty is essential for the application of modern machine learning methods in safety-critical settings. In this regard, the use of credal sets (i.e., convex sets of probability distributions) has recently…

Machine Learning · Computer Science 2026-03-10 Paul Hofman , Timo Löhr , Maximilian Muschalik , Yusuf Sale , Eyke Hüllermeier

General predictive models do not provide a measure of confidence in predictions without Bayesian assumptions. A way to circumvent potential restrictions is to use conformal methods for constructing non-parametric confidence regions, that…

Machine Learning · Statistics 2016-09-21 Evgeny Burnaev , Ivan Nazarov

Conformal prediction has recently emerged as a promising strategy for quantifying the uncertainty of a predictive model; these algorithms modify the model to output sets of labels that are guaranteed to contain the true label with high…

Machine Learning · Computer Science 2025-03-11 Botong Zhang , Shuo Li , Osbert Bastani

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent…

Machine Learning · Computer Science 2025-01-28 Hao Shu , Jicheng Li , Yu Jin , Hailin Wang

Uncertainty is critical to reliable decision-making with machine learning. Conformal prediction (CP) handles uncertainty by predicting a set on a test input, hoping the set to cover the true label with at least $(1-\alpha)$ confidence. This…

Machine Learning · Computer Science 2024-03-25 Rui Xu , Yue Sun , Chao Chen , Parv Venkitasubramaniam , Sihong Xie

When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the…

Machine Learning · Statistics 2022-12-08 Eugene Ndiaye

When building either prediction intervals for regression (with real-valued response) or prediction sets for classification (with categorical responses), uncertainty quantification is essential to studying complex machine learning methods.…

Machine Learning · Statistics 2022-06-17 Chen Xu , Yao Xie

We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard…

Machine Learning · Computer Science 2026-05-11 Fanyi Wu , Veronika Lohmanova , Samuel Kaski , Michele Caprio

Identifying low-dimensional sufficient structures in nonlinear sufficient dimension reduction (SDR) has long been a fundamental yet challenging problem. Most existing methods lack theoretical guarantees of exhaustiveness in identifying…

Machine Learning · Statistics 2025-12-23 Shuntuo Xu , Zhou Yu , Jian Huang

Conformal Prediction (CP) has recently received a tremendous amount of interest, leading to a wide range of new theoretical and methodological results for predictive inference with formal theoretical guarantees. However, the vast majority…

Statistics Theory · Mathematics 2025-08-22 Manit Paul , Arun Kumar Kuchibhotla , Eric J. Tchetgen Tchetgen
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