Related papers: Bayesian with Gaussian process based missing input…

Missing data arises when certain values are not recorded or observed for variables of interest. However, most of the statistical theory assume complete data availability. To address incomplete databases, one approach is to fill the gaps…

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…

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…

We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process.…

A central question in multimodal neuroimaging analysis is to understand the association between two imaging modalities and to identify brain regions where such an association is statistically significant. In this article, we propose a…

Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more…

The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work,…

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

We consider the problem of recovering random graph signals from nonlinear measurements. For this case, closed-form Bayesian estimators are usually intractable and even numerical evaluation of these estimators may be hard to compute for…

In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…

This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…

Bilevel optimization problems can be used to represent the collaborative interaction between a power system and grid-connected entities, called the followers, such as data centers. Most existing approaches assume that such followers'…

Real-world clinical time series data sets exhibit a high prevalence of missing values. Hence, there is an increasing interest in missing data imputation. Traditional statistical approaches impose constraints on the data-generating process…

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…

In this paper we recast the problem of missing values in the covariates of a regression model as a latent Gaussian Markov random field (GMRF) model in a fully Bayesian framework. Our proposed approach is based on the definition of the…

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…

Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of…

A common defect found when reproducing old vinyl and gramophone recordings with mechanical devices are the long pulses with significant low-frequency content caused by the interaction of the arm-needle system with deep scratches or even…