Related papers: Pac-Bayesian Supervised Classification: The Thermo…

Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations…

These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical…

Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…

In unsupervised domain adaptation, it is widely known that the target domain error can be provably reduced by having a shared input representation that makes the source and target domains indistinguishable from each other. Very recently it…

We present a distributionally robust PAC-Bayesian framework for certifying the performance of learning-based finite-horizon controllers. While existing PAC-Bayes control literature typically assumes bounded losses and matching training and…

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

Probabilistic generative modeling of data distributions can potentially exploit hidden information which is useful for discriminative classification. This observation has motivated the development of approaches that couple generative and…

Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…

We study data-driven decision-making problems in the Bayesian framework, where the expectation in the Bayes risk is replaced by a risk-sensitive entropic risk measure. We focus on problems where calculating the posterior distribution is…

Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and…

We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC-Bayes risk certification paradigm. Classifiers are realized as linearly parametrized deep assignment flows with random initial…

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

Recent advances in the field of meta-learning have tackled domains consisting of large numbers of small ("few-shot") supervised learning tasks. Meta-learning algorithms must be able to rapidly adapt to any individual few-shot task, fitting…