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This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

The Bayesian elastic net regression model is characterized by the regression coefficient prior distribution, the negative log density of which corresponds to the elastic net penalty function. While Markov chain Monte Carlo (MCMC) methods…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…

In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

Large crossed mixed effects models with imbalanced structures and missing data pose major computational challenges for standard Bayesian posterior sampling algorithms, as the computational complexity is usually superlinear in the number of…

Generative models have been successfully used for generating realistic signals. Because the likelihood function is typically intractable in most of these models, the common practice is to use "implicit" models that avoid likelihood…

Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…

Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

We propose Deep Neural Coregionalization, a scalable framework for uncertainty-aware multivariate geostatistics. DNC models multivariate spatial effects through spatially varying latent factors and loadings, assigning deep Gaussian process…

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…

Deep generative models (DGMs) have brought about a major breakthrough, as well as renewed interest, in generative latent variable models. However, DGMs do not allow for performing data-driven inference of the number of latent features…

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and…