Related papers: Incertitudes et mesures
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
Uncertainty in machine learning is not generally taught as general knowledge in Machine Learning course curricula. In this paper we propose a short curriculum for a course about uncertainty in machine learning, and complement the course…
This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…
This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental…
Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
Learning unbiased models on imbalanced datasets is a significant challenge. Rare classes tend to get a concentrated representation in the classification space which hampers the generalization of learned boundaries to new test examples. In…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…
We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
Deep Learning sets the state-of-the-art in many challenging tasks showing outstanding performance in a broad range of applications. Despite its success, it still lacks robustness hindering its adoption in medical applications. Modeling…
There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained…
Learning, whether natural or artificial, is a process of selection. It starts with a set of candidate options and selects the more successful ones. In the case of machine learning the selection is done based on empirical estimates of…
We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…