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A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning…

Machine Learning · Statistics 2014-01-14 Mahdi Pakdaman Naeini , Gregory F. Cooper , Milos Hauskrecht

The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be "fair." In…

Machine Learning · Computer Science 2017-11-07 Geoff Pleiss , Manish Raghavan , Felix Wu , Jon Kleinberg , Kilian Q. Weinberger

Calibration requires predictor outputs to be consistent with their Bayesian posteriors. For machine learning predictors that do not distinguish between small perturbations, calibration errors are continuous in predictions, e.g., smooth…

Machine Learning · Computer Science 2025-04-23 Jason Hartline , Yifan Wu , Yunran Yang

We study the fundamental question of how to define and measure the distance from calibration for probabilistic predictors. While the notion of perfect calibration is well-understood, there is no consensus on how to quantify the distance…

Machine Learning · Computer Science 2023-04-03 Jarosław Błasiok , Parikshit Gopalan , Lunjia Hu , Preetum Nakkiran

Recent work has highlighted the centrality of smooth calibration [Kakade and Foster, 2008] as a robust measure of calibration error. We generalize, unify, and extend previous results on smooth calibration, both as a robust calibration…

Machine Learning · Computer Science 2026-03-18 Parikshit Gopalan , Konstantinos Stavropoulos , Kunal Talwar , Pranay Tankala

This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its…

Machine Learning · Computer Science 2023-06-16 Telmo Silva Filho , Hao Song , Miquel Perello-Nieto , Raul Santos-Rodriguez , Meelis Kull , Peter Flach

In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is…

Machine Learning · Statistics 2022-09-30 David Widmann , Fredrik Lindsten , Dave Zachariah

Accurate probabilistic predictions can be characterized by two properties -- calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate -- a 90% confidence interval…

Machine Learning · Computer Science 2025-05-14 Volodymyr Kuleshov , Shachi Deshpande

Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc…

Machine Learning · Computer Science 2023-11-01 Charles Marx , Sofian Zalouk , Stefano Ermon

Despite their impressive predictive performance in various computer vision tasks, deep neural networks (DNNs) tend to make overly confident predictions, which hinders their widespread use in safety-critical applications. While there have…

Computer Vision and Pattern Recognition · Computer Science 2023-12-12 Teodora Popordanoska , Aleksei Tiulpin , Matthew B. Blaschko

Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…

Machine Learning · Computer Science 2024-12-03 Alireza Torabian , Ruth Urner

A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…

Data Analysis, Statistics and Probability · Physics 2020-12-09 Jochen Bröcker

We study a sequential binary prediction setting where the forecaster is evaluated in terms of the calibration distance, which is defined as the $L_1$ distance between the predicted values and the set of predictions that are perfectly…

Machine Learning · Computer Science 2024-05-28 Mingda Qiao , Letian Zheng

Calibration is a well-studied property of predictors which guarantees meaningful uncertainty estimates. Multicalibration is a related notion -- originating in algorithmic fairness -- which requires predictors to be simultaneously calibrated…

Machine Learning · Computer Science 2024-11-06 Dutch Hansen , Siddartha Devic , Preetum Nakkiran , Vatsal Sharan

In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…

Methodology · Statistics 2023-10-16 Richard D. Wilkinson , Christopher W. Lanyon

When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated -- amongst the inputs that receive…

Machine Learning · Statistics 2021-07-14 Shengjia Zhao , Michael P. Kim , Roshni Sahoo , Tengyu Ma , Stefano Ermon

Probabilistic predictions can be evaluated through comparisons with observed label frequencies, that is, through the lens of calibration. Recent scholarship on algorithmic fairness has started to look at a growing variety of…

Machine Learning · Computer Science 2023-05-16 Benedikt Höltgen , Robert C Williamson

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Kennedy and O'Hagan \cite{kennedy2001bayesian} suggested an approach to estimate them by using…

Methodology · Statistics 2015-08-31 Rui Tuo , C. F. Jeff Wu

Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by…

Machine Learning · Computer Science 2020-01-31 Tuomo Alasalmi , Jaakko Suutala , Heli Koskimäki , Juha Röning

Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer…

Machine Learning · Statistics 2020-09-09 Saumya Bhatnagar , Won Chang , Seonjin Kim Jiali Wang