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Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Machine Learning · Computer Science 2024-04-22 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…

Machine Learning · Computer Science 2025-07-24 Jacqueline Maasch , Willie Neiswanger , Stefano Ermon , Volodymyr Kuleshov

The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…

Machine Learning · Computer Science 2026-04-22 Maxim Raginsky , Benjamin Recht

Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…

Machine Learning · Computer Science 2026-03-25 Sébastien Piérard , Anaïs Halin , Anthony Cioppa , Adrien Deliège , Marc Van Droogenbroeck

Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as…

Logic in Computer Science · Computer Science 2025-09-17 Marta Kwiatkowska , Gethin Norman , David Parker

The concept of Probability of Causation (PC) is critically important in legal contexts and can help in many other domains. While it has been around since 1986, current operationalizations can obtain only the minimum and maximum values of…

Methodology · Statistics 2018-08-14 Tapajit Dey , Audris Mockus

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…

Machine Learning · Statistics 2024-03-19 Hristos Tyralis , Georgia Papacharalampous

Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…

Machine Learning · Computer Science 2012-07-02 Harald Steck

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

Machine Learning · Computer Science 2020-02-26 Lukáš Adam , Václav Mácha , Václav Šmídl , Tomáš Pevný

Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…

Machine Learning · Computer Science 2025-12-03 Pieter Smet

We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…

Statistics Theory · Mathematics 2023-01-04 Efrén Cruz Cortés , Kevin Josey , Fan Yang , Debashis Ghosh

Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…

Logic in Computer Science · Computer Science 2026-04-08 Weijun Chen , Yuxi Fu , Huan Long , Hao Wu

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

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for…

Machine Learning · Statistics 2021-04-12 Jan-Matthis Lueckmann , Jan Boelts , David S. Greenberg , Pedro J. Gonçalves , Jakob H. Macke

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

Machine Learning · Computer Science 2024-03-14 Sebastian G. Gruber , Florian Buettner

Predictive models are often introduced to decision-making tasks under the rationale that they improve performance over an existing decision-making policy. However, it is challenging to compare predictive performance against an existing…

Machine Learning · Computer Science 2024-06-13 Luke Guerdan , Amanda Coston , Kenneth Holstein , Zhiwei Steven Wu

We provide methods to validate and compare sensor outputs, or inference algorithms applied to sensor data, by adapting statistical scoring rules. The reported output should either be in the form of a prediction interval or of a parameter…

Data Analysis, Statistics and Probability · Physics 2015-07-07 A. D. Martin , T. C. A. Molteno , M. Parry

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good…

Machine Learning · Computer Science 2023-06-07 Étienne Marcotte , Valentina Zantedeschi , Alexandre Drouin , Nicolas Chapados

With the increased use of machine learning systems for decision making, questions about the fairness properties of such systems start to take center stage. Most existing work on algorithmic fairness assume complete observation of features…

Machine Learning · Computer Science 2022-12-06 Nikil Roashan Selvam , Guy Van den Broeck , YooJung Choi

In this work, we study some novel applications of conformal inference techniques to the problem of providing machine learning procedures with more transparent, accurate, and practical performance guarantees. We provide a natural extension…

Machine Learning · Statistics 2020-07-10 Matthew J. Holland