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Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…
Modern deep neural networks are well known to be brittle in the face of unknown data instances and recognition of the latter remains a challenge. Although it is inevitable for continual-learning systems to encounter such unseen concepts,…
Gaussian processes are a versatile probabilistic machine learning model whose effectiveness often depends on good hyperparameters, which are typically learned by maximising the marginal likelihood. In this work, we consider iterative…
We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential…
We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a…
Inferring parameters and testing hypotheses from gravitational wave signals is a computationally intensive task central to modern astrophysics. Nested sampling, a Bayesian inference technique, has become an established standard for this in…
Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive…
Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…
When modelling censored observations, a typical approach in current regression methods is to use a censored-Gaussian (i.e. Tobit) model to describe the conditional output distribution. In this paper, as in the case of missing data, we argue…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
Infinitely wide or deep neural networks (NNs) with independent and identically distributed (i.i.d.) parameters have been shown to be equivalent to Gaussian processes. Because of the favorable properties of Gaussian processes, this…
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…
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…
Recent advances in neural variational inference have spawned a renaissance in deep latent variable models. In this paper we introduce a generic variational inference framework for generative and conditional models of text. While traditional…
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…