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Calibrated probabilistic classifiers are models whose predicted probabilities can directly be interpreted as uncertainty estimates. It has been shown recently that deep neural networks are poorly calibrated and tend to output overconfident…

Machine Learning · Statistics 2022-10-17 Teodora Popordanoska , Raphael Sayer , Matthew B. Blaschko

Machine-generated probability predictions are essential in modern classification tasks such as image classification. A model is well calibrated when its predicted probabilities correspond to observed event frequencies. Despite the need for…

Machine Learning · Statistics 2026-02-24 Amy Vennos , Xin Xing , Christopher T. Franck

A suitable scalar metric can help measure multi-calibration, defined as follows. When the expected values of observed responses are equal to corresponding predicted probabilities, the probabilistic predictions are known as "perfectly…

Methodology · Statistics 2026-04-17 Ido Guy , Daniel Haimovich , Fridolin Linder , Nastaran Okati , Lorenzo Perini , Niek Tax , Mark Tygert

Calibration weighting has been widely used to correct selection biases in non-probability sampling, missing data, and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights.…

Methodology · Statistics 2023-05-30 Chenyin Gao , Shu Yang , Jae Kwang Kim

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

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…

Machine Learning · Statistics 2023-04-20 Thomas Mortier , Viktor Bengs , Eyke Hüllermeier , Stijn Luca , Willem Waegeman

Developing trustworthy Machine Learning (ML) models requires their predicted probabilities to be well-calibrated, meaning they should reflect true-class frequencies. Among calibration notions in multiclass classification, strong calibration…

Machine Learning · Computer Science 2026-04-22 Cesare Barbera , Lorenzo Perini , Giovanni De Toni , Andrea Passerini , Andrea Pugnana

There is a growing interest in societal concerns in machine learning systems, especially in fairness. Multicalibration gives a comprehensive methodology to address group fairness. In this work, we address the multicalibration error and…

Machine Learning · Computer Science 2021-06-08 Eliran Shabat , Lee Cohen , Yishay Mansour

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

A multiclass classifier is said to be top-label calibrated if the reported probability for the predicted class -- the top-label -- is calibrated, conditioned on the top-label. This conditioning on the top-label is absent in the closely…

Machine Learning · Computer Science 2022-09-07 Chirag Gupta , Aaditya Ramdas

Extreme multilabel classification (XMLC) problems occur in settings such as related product recommendation, large-scale document tagging, or ad prediction, and are characterized by a label space that can span millions of possible labels.…

Machine Learning · Computer Science 2024-11-08 Nasib Ullah , Erik Schultheis , Jinbin Zhang , Rohit Babbar

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

Pretrained multilingual encoder models can directly perform zero-shot multilingual tasks or linguistic probing by reformulating the input examples into cloze-style prompts. This is accomplished by predicting the probabilities of the label…

Computation and Language · Computer Science 2023-10-20 Ercong Nie , Helmut Schmid , Hinrich Schütze

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike…

Machine Learning · Computer Science 2017-08-04 Chuan Guo , Geoff Pleiss , Yu Sun , Kilian Q. Weinberger

As machine learning models are increasingly deployed in high-stakes environments, ensuring both probabilistic reliability and prediction stability has become critical. This paper examines the interplay between classification calibration and…

Machine Learning · Computer Science 2026-03-17 Mustafa Cavus

One prominent method of evaluating machine learning model trustworthiness is the notion of calibration. In the binary outcome setting, a probabilistic predictor is calibrated if outcomes are realized according to a model's distributional…

Machine Learning · Computer Science 2026-05-25 Jessica Finocchiaro , Victor Ganson , Drona Khurana

Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…

Machine Learning · Statistics 2026-03-04 Ilia Azizi , Juraj Bodik , Jakob Heiss , Bin Yu

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective…

Machine Learning · Computer Science 2019-10-29 Meelis Kull , Miquel Perello-Nieto , Markus Kängsepp , Telmo Silva Filho , Hao Song , Peter Flach

While the performance of machine learning systems has experienced significant improvement in recent years, relatively little attention has been paid to the fundamental question: to what extent can we improve our models? This paper provides…

Machine Learning · Computer Science 2026-05-13 Ryota Ushio , Takashi Ishida , Masashi Sugiyama

Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…

Information Retrieval · Computer Science 2018-03-06 Michiel Stock , Krzysztof Dembczynski , Bernard De Baets , Willem Waegeman