Related papers: Functional regression approximate Bayesian computa…

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such…

We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…

Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…

Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…

In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…

In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process…

This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general…

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…

This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…

We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…

Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…