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We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…

Although an ever-growing number of applications employ deep learning based systems for prediction, decision-making, or state estimation, almost no certification processes have been established that would allow such systems to be deployed in…

Machine Learning · Computer Science 2024-03-25 Romeo Valentin

Machine learning models typically focus on specific targets like creating classifiers, often based on known population feature distributions in a business context. However, models calculating individual features adapt over time to improve…

Machine Learning · Computer Science 2024-02-23 Emanuele Luzio , Moacir Antonelli Ponti , Christian Ramirez Arevalo , Luis Argerich

While the accuracy of modern deep learning models has significantly improved in recent years, the ability of these models to generate uncertainty estimates has not progressed to the same degree. Uncertainty methods are designed to provide…

Machine Learning · Statistics 2020-06-17 Adam M. Oberman , Chris Finlay , Alexander Iannantuono , Tiago Salvador

Analyzing classification model performance is a crucial task for machine learning practitioners. While practitioners often use count-based metrics derived from confusion matrices, like accuracy, many applications, such as weather…

Human-Computer Interaction · Computer Science 2022-07-29 Peter Xenopoulos , Joao Rulff , Luis Gustavo Nonato , Brian Barr , Claudio Silva

We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the…

Machine Learning · Statistics 2021-03-01 Haoxian Chen , Ziyi Huang , Henry Lam , Huajie Qian , Haofeng Zhang

This paper aims at one-shot learning of deep neural nets, where a highly parallel setting is considered to address the algorithm calibration problem - selecting the best neural architecture and learning hyper-parameter values depending on…

Machine Learning · Computer Science 2017-06-21 Olivier Bousquet , Sylvain Gelly , Karol Kurach , Marc Schoenauer , Michele Sebag , Olivier Teytaud , Damien Vincent

The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not…

Machine Learning · Statistics 2018-06-21 Hao Song , Meelis Kull , Peter Flach

Generalization is a central problem in Machine Learning. Indeed most prediction methods require careful calibration of hyperparameters usually carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of…

Machine Learning · Statistics 2021-02-18 Karim Lounici , Katia Meziani , Benjamin Riu

Ensuring that classifiers are well-calibrated, i.e., their predictions align with observed frequencies, is a minimal and fundamental requirement for classifiers to be viewed as trustworthy. Existing methods for assessing multiclass…

Machine Learning · Computer Science 2025-10-30 Mahmoud Hegazy , Michael I. Jordan , Aymeric Dieuleveut

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

When providing probabilistic forecasts for uncertain future events, it is common to strive for calibrated forecasts, that is, the predictive distribution should be compatible with the observed outcomes. Several notions of calibration are…

Methodology · Statistics 2015-05-21 Christof Strähl , Johanna F. Ziegel

Optimal control strategies are often combined with safety certificates to ensure both performance and safety in safety-critical systems. A prominent example is combining Model Predictive Control (MPC) with Control Barrier Functions (CBF).…

Systems and Control · Electrical Eng. & Systems 2025-12-05 Kerim Dzhumageldyev , Filippo Airaldi , Azita Dabiri

Modern machine learning models with high accuracy are often miscalibrated -- the predicted top probability does not reflect the actual accuracy, and tends to be over-confident. It is commonly believed that such over-confidence is mainly due…

Machine Learning · Computer Science 2021-07-21 Yu Bai , Song Mei , Huan Wang , Caiming Xiong

Generative classifiers are constructed on the basis of a joint probability distribution and are typically learned using closed-form procedures that rely on data statistics and maximize scores related to data fitting. However, these scores…

Machine Learning · Computer Science 2025-03-31 Aritz Pérez , Carlos Echegoyen , Guzmán Santafé

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

Calibration of neural networks is a topical problem that is becoming more and more important as neural networks increasingly underpin real-world applications. The problem is especially noticeable when using modern neural networks, for which…

Machine Learning · Computer Science 2023-08-29 Ondrej Bohdal , Yongxin Yang , Timothy Hospedales

As machine learning techniques become widely adopted in new domains, especially in safety-critical systems such as autonomous vehicles, it is crucial to provide accurate output uncertainty estimation. As a result, many approaches have been…

Machine Learning · Computer Science 2021-12-28 Sooyong Jang , Radoslav Ivanov , Insup Lee , James Weimer

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

Machine Learning · Computer Science 2018-07-03 Volodymyr Kuleshov , Nathan Fenner , Stefano Ermon

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
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