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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

Unlike the typical classification setting where each instance is associated with a single class, in multi-label learning each instance is associated with multiple classes simultaneously. Therefore the learning task in this setting is to…

Machine Learning · Computer Science 2022-11-30 Harris Papadopoulos

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

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

Complementary-Label Learning (CLL) is a weakly-supervised learning problem that aims to learn a multi-class classifier from only complementary labels, which indicate a class to which an instance does not belong. Existing approaches mainly…

Machine Learning · Computer Science 2023-04-12 Wei-I Lin , Hsuan-Tien Lin

In a split conformal framework with $K$ classes, a calibration sample of $n$ labeled examples is observed for inference on the label of a new unlabeled example. We explore the setting where a `batch' of $m$ independent such unlabeled…

Methodology · Statistics 2025-03-19 Ulysse Gazin , Ruth Heller , Etienne Roquain , Aldo Solari

Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or…

Machine Learning · Computer Science 2024-12-06 Disha Ghandwani , Neeraj Sarna , Yuanyuan Li , Yang Lin

A machine learning model is calibrated if its predicted probability for an outcome matches the observed frequency for that outcome conditional on the model prediction. This property has become increasingly important as the impact of machine…

Machine Learning · Computer Science 2025-02-25 Muthu Chidambaram , Rong Ge

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is…

Machine Learning · Statistics 2023-12-07 Donghwan Lee , Xinmeng Huang , Hamed Hassani , Edgar Dobriban

In many applications, accurate class probability estimates are required, but many types of models produce poor quality probability estimates despite achieving acceptable classification accuracy. Even though probability calibration has been…

Machine Learning · Computer Science 2020-02-18 Tim Leathart , Maksymilian Polaczuk

Accurate and reliable probability predictions are essential for multi-class supervised learning tasks, where well-calibrated models enable rational decision-making. While isotonic regression has proven effective for binary calibration, its…

Machine Learning · Computer Science 2025-12-11 Alon Arad , Saharon Rosset

The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…

Machine Learning · Computer Science 2014-05-13 Amit Daniely , Shai Shalev-Shwartz

Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing,…

Machine Learning · Computer Science 2020-11-17 Christos Thrampoulidis , Samet Oymak , Mahdi Soltanolkotabi

We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a…

Machine Learning · Computer Science 2025-10-15 Isaac Gibbs , Ryan J. Tibshirani

Recent studies have revealed that, beyond conventional accuracy, calibration should also be considered for training modern deep neural networks. To address miscalibration during learning, some methods have explored different penalty…

Computer Vision and Pattern Recognition · Computer Science 2023-04-13 Bingyuan Liu , Jérôme Rony , Adrian Galdran , Jose Dolz , Ismail Ben Ayed

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

The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting. Motivated by this discrepancy, we…

Machine Learning · Statistics 2023-07-13 Ke Wang , Vidya Muthukumar , Christos Thrampoulidis

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

We investigate the problem of multiclass classification with rejection, where a classifier can choose not to make a prediction to avoid critical misclassification. First, we consider an approach based on simultaneous training of a…

Machine Learning · Statistics 2019-10-31 Chenri Ni , Nontawat Charoenphakdee , Junya Honda , Masashi Sugiyama

Multi-label classification consists in classifying an instance into two or more classes simultaneously. It is a very challenging task present in many real-world applications, such as classification of biology, image, video, audio, and text.…

Machine Learning · Computer Science 2020-04-03 Thiago Zafalon Miranda , Diorge Brognara Sardinha , Márcio Porto Basgalupp , Yaochu Jin , Ricardo Cerri