Related papers: Weighted Fisher divergence for high-dimensional Ga…

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The…

We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…

We derive a single pass algorithm for computing the gradient and Fisher information of Vecchia's Gaussian process loglikelihood approximation, which provides a computationally efficient means for applying the Fisher scoring algorithm for…

Variational representations of $f$-divergences are central to many machine learning algorithms, with Lipschitz constrained variants recently gaining attention. Inspired by this, we define the Moreau-Yosida approximation of $f$-divergences…

Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies within the class of multifidelity problems, where a variety…

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…

We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with…

One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…

In this paper, we compare the performance of two methods for estimating Bayesian networks from data containing exogenous variables and random effects. The first method is fully Bayesian in which a prior distribution is placed on the…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of $10^5$ ~ $10^6$ and of $10^4$ ~ $10^5$. Despite the large sample size, data rarely provide…

High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…

In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this…