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Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class…

Machine Learning · Computer Science 2024-06-11 Parikshit Gopalan , Lunjia Hu , Guy N. Rothblum

When providing probabilistic forecasts for uncertain future events, it is common to strive for calibrated forecasts, that is, the predictive distribution should be compatible with the observed outcomes. Several notions of calibration are…

Methodology · Statistics 2015-05-21 Christof Strähl , Johanna F. Ziegel

Modern neural networks have found to be miscalibrated in terms of confidence calibration, i.e., their predicted confidence scores do not reflect the observed accuracy or precision. Recent work has introduced methods for post-hoc confidence…

Computer Vision and Pattern Recognition · Computer Science 2021-09-22 Fabian Küppers , Jan Kronenberger , Jonas Schneider , Anselm Haselhoff

Modern deep learning reconstruction algorithms generate impressively realistic scans from sparse inputs, but can often produce significant inaccuracies. This makes it difficult to provide statistically guaranteed claims about the true state…

Machine Learning · Computer Science 2025-09-29 Matt Y Cheung , Tucker J Netherton , Laurence E Court , Ashok Veeraraghavan , Guha Balakrishnan

Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating…

Machine Learning · Computer Science 2025-09-23 Wenjian Huang , Guiping Cao , Jiahao Xia , Jingkun Chen , Hao Wang , Jianguo Zhang

We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…

Machine Learning · Statistics 2023-01-18 Tengyuan Liang

We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…

Methodology · Statistics 2018-09-26 Xiaowu Dai , Peter Chien

Conformal prediction (CP) converts any model's output to prediction sets with a guarantee to cover the true label with (adjustable) high probability. Robust CP extends this guarantee to worst-case (adversarial) inputs. Existing baselines…

Machine Learning · Computer Science 2025-03-10 Soroush H. Zargarbashi , Aleksandar Bojchevski

Ensuring that predicted probabilities align with observed frequencies is critical in high-stakes domains such as clinical decision support, autonomous driving and financial risk assessment. Existing calibration methods typically apply a…

Machine Learning · Computer Science 2026-05-26 Tomer Lavi , Bracha Shapira , Nadav Rappoport

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating…

Machine Learning · Computer Science 2022-10-03 Anastasios N. Angelopoulos , Stephen Bates , Emmanuel J. Candès , Michael I. Jordan , Lihua Lei

Delivering meaningful uncertainty estimates is essential for a successful deployment of machine learning models in the clinical practice. A central aspect of uncertainty quantification is the ability of a model to return predictions that…

Computer Vision and Pattern Recognition · Computer Science 2023-03-03 Adrian Galdran , Johan Verjans , Gustavo Carneiro , Miguel A. González Ballester

Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two…

Machine Learning · Computer Science 2021-12-30 Kartik Gupta , Amir Rahimi , Thalaiyasingam Ajanthan , Thomas Mensink , Cristian Sminchisescu , Richard Hartley

A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two…

Methodology · Statistics 2023-10-27 Caren Hasler

In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…

Machine Learning · Statistics 2022-06-22 Ambrus Tamás , Balázs Csanád Csáji

Despite extensive research on neural network calibration, existing methods typically apply global transformations that treat all predictions uniformly, overlooking the heterogeneous reliability of individual predictions. Furthermore, the…

Machine Learning · Computer Science 2025-10-22 Hassan Gharoun , Mohammad Sadegh Khorshidi , Kasra Ranjbarigderi , Fang Chen , Amir H. Gandomi

We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting, that is without making any distributional assumptions on the data.…

Machine Learning · Statistics 2022-02-17 Chirag Gupta , Aleksandr Podkopaev , Aaditya Ramdas

Optimizing proper loss functions is popularly believed to yield predictors with good calibration properties; the intuition being that for such losses, the global optimum is to predict the ground-truth probabilities, which is indeed…

Machine Learning · Computer Science 2023-12-11 Jarosław Błasiok , Parikshit Gopalan , Lunjia Hu , Preetum Nakkiran

Fueled by discussions around "trustworthiness" and algorithmic fairness, calibration of predictive systems has regained scholars attention. The vanilla definition and understanding of calibration is, simply put, on all days on which the…

Machine Learning · Computer Science 2025-04-28 Rabanus Derr , Jessie Finocchiaro , Robert C. Williamson

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

Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably…

Machine Learning · Statistics 2025-10-28 Naomi Desobry , Elnura Zhalieva , Souhaib Ben Taieb
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