Related papers: Generalised Bayes Updates with $f$-divergences thr…

Deviations from Bayesian updating are traditionally categorized as biases, errors, or fallacies, thus implying their inherent ``sub-optimality.'' We offer a more nuanced view. We demonstrate that, in learning problems with misspecified…

A learned generative model often produces biased statistics relative to the underlying data distribution. A standard technique to correct this bias is importance sampling, where samples from the model are weighted by the likelihood ratio…

In this paper authors present a general methodology for age dependent reliability analysis of degrading or ageing systems, structures and components.The methodology is based on Bayesian methods and inference, its ability to incorporate…

A robust estimation framework for binary regression models is studied, aiming to extend traditional approaches like logistic regression models. While previous studies largely focused on logistic models, we explore a broader class of models…

We study Bayesian discriminative inference given a model family $p(c,\x, \theta)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and…

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…

Belief Propagation (BP) is one of the most popular methods for inference in probabilistic graphical models. BP is guaranteed to return the correct answer for tree structures, but can be incorrect or non-convergent for loopy graphical…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

We provide a reason for Bayesian updating, in the Bernoulli case, even when it is assumed that observations are independent and identically distributed with a fixed but unknown parameter $\theta_0$. The motivation relies on the use of loss…

Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…

As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…

Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian…

Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…

This paper reviews the basic ideas behind a Bayesian unfolding published some years ago and improves their implementation. In particular, uncertainties are now treated at all levels by probability density functions and their propagation is…

Fairness-aware learning is a novel framework for classification tasks. Like regular empirical risk minimization (ERM), it aims to learn a classifier with a low error rate, and at the same time, for the predictions of the classifier to be…

Belief and plausibility are weaker measures of uncertainty than that of probability. They are motivated by the situations when full probabilistic information is not available. However, information can also be contradictory. Therefore, the…

In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measures or regularizations are…

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…