Related papers: Hilbert space methods for approximating multi-outp…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued…

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…

Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…

We consider Proximal Newton methods with an inexact computation of update steps. To this end, we introduce two inexactness criteria which characterize sufficient accuracy of these update step and with the aid of these investigate global…

Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…

We present a unified view of likelihood based Gaussian progress regression for simulation experiments exhibiting input-dependent noise. Replication plays an important role in that context, however previous methods leveraging replicates have…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller…

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…

Machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational…

Gaussian processes are now commonly used in dimensionality reduction approaches tailored to neuroscience, especially to describe changes in high-dimensional neural activity over time. As recording capabilities expand to include neuronal…

We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of…

Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…