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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

In this work, we investigate the reliability of the probabilistic binary forecast. We mathematically prove that a necessary, but not sufficient, condition for achieving a reliable probabilistic forecast is maximizing the Peirce skill score…

Space Physics · Physics 2019-05-20 Yûki Kubo

Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…

Methodology · Statistics 2025-12-01 Haiyi Shi , Lei Yang , Jiarui Chi , Troy Butler , Haonan Wang , Derek Bingham , Don Estep

Measures of accuracy usually score how accurate a specified credence depending on whether the proposition is true or false. A key requirement for such measures is strict propriety; that probabilities expect themselves to be most accurate.…

Probability · Mathematics 2024-12-11 Catrin Campbell-Moore

Underlying the use of statistical approaches for a wide range of applications is the assumption that the probabilities obtained from a statistical model are representative of the "true" probability that event, or outcome, will occur.…

Machine Learning · Computer Science 2021-01-15 Xixin Wu , Mark Gales

Predictability is an emerging metric that quantifies the highest possible prediction accuracy for a given time series, being widely utilized in assessing known prediction algorithms and characterizing intrinsic regularities in human…

Information Theory · Computer Science 2023-03-29 En Xu , Tao Zhou , Zhiwen Yu , Zhuo Sun , Bin Guo

Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a…

Applications · Statistics 2022-07-22 Carl Boettiger

Trained DNN models are increasingly adopted as integral parts of software systems, but they often perform deficiently in the field. A particularly damaging problem is that DNN models often give false predictions with high confidence, due to…

Machine Learning · Computer Science 2020-09-16 Zenan Li , Xiaoxing Ma , Chang Xu , Jingwei Xu , Chun Cao , Jian Lü

Modern convolutional neural networks (CNNs) are known to be overconfident in terms of their calibration on unseen input data. That is to say, they are more confident than they are accurate. This is undesirable if the probabilities predicted…

Machine Learning · Computer Science 2021-12-03 Guoxuan Xia , Sangwon Ha , Tiago Azevedo , Partha Maji

The predictability of errors in deterministic temperature forecasts is investigated. More precisely, the aim is to issue warnings whenever the differences between forecast and verification exceed a given threshold. The warnings are…

Atmospheric and Oceanic Physics · Physics 2011-12-08 S. Hallerberg , J. Bröcker , H. Kantz , L. A. Smith

This paper develops a Bayesian network-based method for the calibration of multi-physics models, integrating various sources of uncertainty with information from computational models and experimental data. We adopt the Kennedy and O'Hagan…

Data Analysis, Statistics and Probability · Physics 2012-06-25 You Ling , Joshua Mullins , Sankaran Mahadevan

Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…

Methodology · Statistics 2017-05-10 Rui Tuo

Kennedy and O'Hagan (2001) propose a model for calibrating some unknown parameters in a computer model and estimating the discrepancy between the computer output and physical response. This model is known to have certain identifiability…

Statistics Theory · Mathematics 2017-03-07 Rui Tuo , C. F. Jeff Wu

Conformal predictors are machine learning algorithms developed in the 1990's by Gammerman, Vovk, and their research team, to provide set predictions with guaranteed confidence level. Over recent years, they have grown in popularity and have…

Machine Learning · Computer Science 2025-08-12 Anthony Bellotti , Xindi Zhao

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…

Machine Learning · Statistics 2019-11-01 Jayaraman J. Thiagarajan , Bindya Venkatesh , Deepta Rajan

For users to trust model predictions, they need to understand model outputs, particularly their confidence - calibration aims to adjust (calibrate) models' confidence to match expected accuracy. We argue that the traditional calibration…

Computation and Language · Computer Science 2022-10-25 Chenglei Si , Chen Zhao , Sewon Min , Jordan Boyd-Graber

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

The weighted average is by far the most popular approach to combining multiple forecasts of some future outcome. This paper shows that both for probability or real-valued forecasts, a non-trivial weighted average of different forecasts is…

Methodology · Statistics 2015-09-28 Ville Satopää , Lyle Ungar

We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration…

Theoretical Economics · Economics 2022-10-14 Dean P. Foster , Sergiu Hart

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