Related papers: Non-Stationary Multi-layered Gaussian Priors for B…
In this paper, we study Bayesian approach for solving large scale linear inverse problems arising in various scientific and engineering fields. We propose a fused $L_{1/2}$ prior with edge-preserving and sparsity-promoting properties and…
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
In many large-scale inverse problems, such as computed tomography and image deblurring, characterization of sharp edges in the solution is desired. Within the Bayesian approach to inverse problems, edge-preservation is often achieved using…
Bayesian Neural Networks represent a fascinating confluence of deep learning and probabilistic reasoning, offering a compelling framework for understanding uncertainty in complex predictive models. In this paper, we investigate the use of…
We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…
This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by…
This paper considers the problem of iterative Bayesian smoothing in nonlinear state-space models with additive noise using Gaussian approximations. Iterative methods are known to improve smoothed estimates but are not guaranteed to…
This paper deals with the Gaussian process based approximation of a code which can be run at different levels of accuracy. This method, which is a particular case of co-kriging, allows us to improve a surrogate model of a complex computer…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…
Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…
Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated…