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Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

Probability · Mathematics 2012-04-05 Jinqiao Duan , Ting Gao , Guowei He

This work addresses the challenge of providing consistent explanations for predictive models in the presence of model indeterminacy, which arises due to the existence of multiple (nearly) equally well-performing models for a given dataset…

Machine Learning · Computer Science 2023-06-14 Dan Ley , Leonard Tang , Matthew Nazari , Hongjin Lin , Suraj Srinivas , Himabindu Lakkaraju

In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…

Artificial Intelligence · Computer Science 2014-01-16 Marco Zaffalon , Enrique Miranda

The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction…

Computer Vision and Pattern Recognition · Computer Science 2024-06-14 Paul Melki , Lionel Bombrun , Boubacar Diallo , Jérôme Dias , Jean-Pierre da Costa

The calibration of predictive distributions has been widely studied in deep learning, but the same cannot be said about the more specific epistemic uncertainty as produced by Deep Ensembles, Bayesian Deep Networks, or Evidential Deep…

Machine Learning · Computer Science 2024-07-18 Mohammed Fellaji , Frédéric Pennerath , Brieuc Conan-Guez , Miguel Couceiro

Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…

Other Statistics · Statistics 2017-04-26 Grey Nearing , Hoshin Gupta

Causality has traditionally been a scientific way to generate knowledge by relating causes to effects. From an imaginery point of view, causal graphs are a helpful tool for representing and infering new causal information. In previous…

Artificial Intelligence · Computer Science 2020-02-07 Eduardo C. Garrido-Merchán , C. Puente , A. Sobrino , J. A. Olivas

Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…

Machine Learning · Statistics 2026-02-10 Anchit Jain , Stephen Bates

The comparisons of uncertainty calculi from the last two Uncertainty Workshops have all used theoretical probabilistic accuracy as the sole metric. While mathematical correctness is important, there are other factors which should be…

Artificial Intelligence · Computer Science 2013-04-11 Donald H. Mitchell , Steven A. Harp , David K. Simkin

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in…

Computation and Language · Computer Science 2023-04-18 Lorenz Kuhn , Yarin Gal , Sebastian Farquhar

Comparing alternatives in pairs is a well-known method of ranking creation. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is prepared. As experts conduct the individual…

Discrete Mathematics · Computer Science 2018-12-12 Konrad Kułakowski

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…

Machine Learning · Computer Science 2025-06-17 Kajetan Schweighofer , Lukas Aichberger , Mykyta Ielanskyi , Sepp Hochreiter

We introduce a set of resampling-based methods for quantifying uncertainty and statistical precision of evaluation metrics in multilingual and/or multitask NLP benchmarks. We show how experimental variation in performance scores arises from…

Computation and Language · Computer Science 2025-12-19 Jonne Sälevä , Duygu Ataman , Constantine Lignos

Feature attribution methods help make machine learning-based inference explainable by determining how much one or several features have contributed to a model's output. A particularly popular attribution method is based on the Shapley value…

Artificial Intelligence · Computer Science 2025-11-04 Filip Naudot , Tobias Sundqvist , Timotheus Kampik

Mathematical analysis of the analytic hierarchy process (AHP) led to the development of a mathematical function, usually called the inconsistency index, which has the center role in measuring the inconsistency of the judgements in AHP.…

Logic in Computer Science · Computer Science 2024-08-27 Sangeeta Pant , Anuj Kumar , Jiří Mazurek

Detecting and measuring confounding effects from data is a key challenge in causal inference. Existing methods frequently assume causal sufficiency, disregarding the presence of unobserved confounding variables. Causal sufficiency is both…

Artificial Intelligence · Computer Science 2024-09-27 Abbavaram Gowtham Reddy , Vineeth N Balasubramanian

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…

Machine Learning · Computer Science 2021-11-17 Emily Black , Klas Leino , Matt Fredrikson

The Shapley value, originating from cooperative game theory, has been employed to define responsibility measures that quantify the contributions of database facts to obtaining a given query answer. For non-numeric queries, this is done by…

Databases · Computer Science 2026-01-19 Meghyn Bienvenu , Diego Figueira , Pierre Lafourcade

This paper explores generalised probabilistic modelling and uncertainty estimation in comparative LLM-as-a-judge frameworks. We show that existing Product-of-Experts methods are specific cases of a broader framework, enabling diverse…

Artificial Intelligence · Computer Science 2025-05-22 Yassir Fathullah , Mark J. F. Gales

In causal inference, confounders are variables that influence both treatment decisions and outcomes. However, unlike as in randomized clinical trials, the treatment assignment mechanism in observational studies is not known, and it is thus…

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