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Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification,…

Machine Learning · Computer Science 2021-03-16 Eric Zelikman , Christopher Healy , Sharon Zhou , Anand Avati

Machine learning applications often require calibrated predictions, e.g. a 90\% credible interval should contain the true outcome 90\% of the times. However, typical definitions of calibration only require this to hold on average, and offer…

Machine Learning · Statistics 2020-09-10 Shengjia Zhao , Tengyu Ma , Stefano Ermon

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

In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…

Machine Learning · Computer Science 2025-02-11 Yijin Ni , Xiaoming Huo

Being cautious is crucial for enhancing the trustworthiness of machine learning systems integrated into decision-making pipelines. Although calibrated probabilities help in optimal decision-making, perfect calibration remains unattainable,…

Machine Learning · Computer Science 2024-08-12 Mari-Liis Allikivi , Joonas Järve , Meelis Kull

For an AI system to be reliable, the confidence it expresses in its decisions must match its accuracy. To assess the degree of match, examples are typically binned by confidence and the per-bin mean confidence and accuracy are compared.…

Machine Learning · Computer Science 2022-02-14 Rebecca Roelofs , Nicholas Cain , Jonathon Shlens , Michael C. Mozer

In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…

Machine Learning · Statistics 2023-11-07 Hao Zhang

Optimal decision making requires that classifiers produce uncertainty estimates consistent with their empirical accuracy. However, deep neural networks are often under- or over-confident in their predictions. Consequently, methods have been…

Model diagnostics and forecast evaluation are two sides of the same coin. A common principle is that fitted or predicted distributions ought to be calibrated or reliable, ideally in the sense of auto-calibration, where the outcome is a…

Methodology · Statistics 2024-09-27 Tilmann Gneiting , Johannes Resin

In a well-calibrated risk prediction model, the average predicted probability is close to the true event rate for any given subgroup. Such models are reliable across heterogeneous populations and satisfy strong notions of algorithmic…

Machine Learning · Computer Science 2023-07-31 Jean Feng , Alexej Gossmann , Romain Pirracchio , Nicholas Petrick , Gene Pennello , Berkman Sahiner

Reliable precipitation nowcasting is critical for weather-sensitive decision-making, yet neural weather models (NWMs) can produce poorly calibrated probabilistic forecasts. Standard calibration metrics such as the expected calibration error…

Machine Learning · Computer Science 2025-12-01 Lauri Kurki , Yaniel Cabrera , Samu Karanko

Counterfactual inference has become a ubiquitous tool in online advertisement, recommendation systems, medical diagnosis, and econometrics. Accurate modeling of outcome distributions associated with different interventions -- known as…

Machine Learning · Statistics 2021-07-13 Krikamol Muandet , Motonobu Kanagawa , Sorawit Saengkyongam , Sanparith Marukatat

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

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…

Machine Learning · Computer Science 2019-02-20 Juozas Vaicenavicius , David Widmann , Carl Andersson , Fredrik Lindsten , Jacob Roll , Thomas B. Schön

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…

Machine Learning · Computer Science 2025-07-30 Mira Jürgens , Thomas Mortier , Eyke Hüllermeier , Viktor Bengs , Willem Waegeman

Deep time-series forecasting can be formulated as a distribution balancing problem aimed at aligning the distribution of the forecasts and ground truths. According to Imbens' criterion, true distribution balance requires matching the first…

Machine Learning · Computer Science 2026-02-03 Licheng Pan , Hao Wang , Haocheng Yang , Yuqi Li , Qingsong Wen , Xiaoxi Li , Zhichao Chen , Haoxuan Li , Zhixuan Chu , Yuan Lu

Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the…

Statistics Theory · Mathematics 2023-01-11 Timo Dimitriadis , Lutz Duembgen , Alexander Henzi , Marius Puke , Johanna Ziegel

The adoption of deep learning across various fields has been extensive, yet there is a lack of focus on evaluating the performance of deep learning pipelines. Typically, with the increased use of large datasets and complex models, the…

Machine Learning · Computer Science 2024-05-21 Yewen Fan , Nian Si , Xiangchen Song , Kun Zhang

In next-generation communications and networks, machine learning (ML) models are expected to deliver not only accurate predictions but also well-calibrated confidence scores that reflect the true likelihood of correct decisions. This paper…

Machine Learning · Statistics 2025-11-21 Rashika Raina , Nidhi Simmons , David E. Simmons , Michel Daoud Yacoub , Trung Q. Duong

Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures…

Machine Learning · Computer Science 2020-08-11 Jeremy Nixon , Mike Dusenberry , Ghassen Jerfel , Timothy Nguyen , Jeremiah Liu , Linchuan Zhang , Dustin Tran
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