Related papers: Incertitudes et mesures
Artificial neural networks will always make a prediction, even when completely uncertain and regardless of the consequences. This obliviousness of uncertainty is a major obstacle towards their adoption in practice. Techniques exist,…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
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…
The booklet contain an overview on selected recent developments in nonequilibrium statistical mechanics and chaos theory: SRB distributions, chaotic hypothesis, fluctuation theorem, proposals for tests and applications to granular…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…
The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact,…
In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…
Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in…
Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
We introduce a framework for uncertainty estimation that both describes and extends many existing methods. We consider typical hyperparameters involved in classical training as random variables and marginalise them out to capture various…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
Tensors, also known as multidimensional arrays, are useful data structures in machine learning and statistics. In recent years, Bayesian methods have emerged as a popular direction for analyzing tensor-valued data since they provide a…
Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
Understanding data and reaching valid conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have widespread application for this purpose in different fields. One critically…