Related papers: Bayesian computation for high-dimensional Gaussian…

Gaussian Process Regression (GPR) is widely used for inferring functions from noisy data. GPR crucially relies on the choice of a kernel, which might be specified in terms of a collection of hyperparameters that must be chosen or learned.…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…

Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…

Selecting interpretable feature sets in underdetermined ($n \ll p$) and highly correlated regimes constitutes a fundamental challenge in data science, particularly when analyzing physical measurements. In such settings, multiple distinct…

Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…

This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters $K$ and the set of…

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…

Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the…

We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use…

Covariate-dependent graph learning has gained increasing interest in the graphical modeling literature for the analysis of heterogeneous data. This task, however, poses challenges to modeling, computational efficiency, and interpretability.…