Related papers: Nested Expectation Propagation for Gaussian Proces…

A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…

Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…

We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a…

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…

Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…

In this paper we consider the problem of Gaussian process classifier (GPC) model selection with different Leave-One-Out (LOO) Cross Validation (CV) based optimization criteria and provide a practical algorithm using LOO predictive…

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…

We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…

Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…

It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly…

This paper presents a new Expectation Propagation (EP) framework for image restoration using patch-based prior distributions. While Monte Carlo techniques are classically used to sample from intractable posterior distributions, they can…

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…

Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…

Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is…

Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also…

Learning using privileged information is an attractive problem setting that helps many learning scenarios in the real world. A state-of-the-art method of Gaussian process classification (GPC) with privileged information is GPC+, which…

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…