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ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

Machine Learning · Statistics 2025-09-23 Xiaoping Du

Predictive uncertainty estimation of pre-trained language models is an important measure of how likely people can trust their predictions. However, little is known about what makes a model prediction uncertain. Explaining predictive…

Computation and Language · Computer Science 2022-10-11 Hanjie Chen , Wanyu Du , Yangfeng Ji

Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such…

Artificial Intelligence · Computer Science 2017-12-27 Fattaneh Jabbari , Mahdi Pakdaman Naeini , Gregory F. Cooper

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…

Statistics Theory · Mathematics 2017-05-24 Samuel N. Cohen

Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either…

Optimization and Control · Mathematics 2022-02-23 Omid Nohadani , Kartikey Sharma

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

Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds…

Statistics Theory · Mathematics 2007-08-22 Chang Xuan Mao , Bruce G. Lindsay

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…

Artificial Intelligence · Computer Science 2014-05-26 Phil Maguire , Philippe Moser , Rebecca Maguire , Mark Keane

Comparisons are made for the amount of agreement of the composite likelihood information criteria and their full likelihood counterparts when making decisions among the fits of different models, and some properties of penalty term for…

Statistics Theory · Mathematics 2014-10-17 Chi Tim Ng , Harry Joe

This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty…

Artificial Intelligence · Computer Science 2023-03-13 Thom Badings , Thiago D. Simão , Marnix Suilen , Nils Jansen

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

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

Artificial Intelligence · Computer Science 2013-04-08 Henri Farrency , Henri Prade

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

Large language models (LLMs) often generate fluent but factually incorrect outputs, known as hallucinations, which undermine their reliability in real-world applications. While uncertainty estimation has emerged as a promising strategy for…

Machine Learning · Computer Science 2025-05-13 Pei-Fu Guo , Yun-Da Tsai , Shou-De Lin

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

Machine Learning · Statistics 2023-02-22 Marvin Schmitt , Stefan T. Radev , Paul-Christian Bürkner

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…

Machine Learning · Statistics 2024-06-05 Laurens Sluijterman , Eric Cator , Tom Heskes

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…

Methodology · Statistics 2023-05-25 Michael Oberst , Alexander D'Amour , Minmin Chen , Yuyan Wang , David Sontag , Steve Yadlowsky

With rapid adoption of deep learning in critical applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account…

Machine Learning · Statistics 2019-11-22 Jayaraman J. Thiagarajan , Bindya Venkatesh , Prasanna Sattigeri , Peer-Timo Bremer

Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…

Machine Learning · Computer Science 2023-09-12 Lucas Clarté , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová