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Gaussian processes (GPs) offer appealing properties but are costly to train at scale. Sparse variational GP (SVGP) approximations reduce cost yet still rely on Cholesky decompositions of kernel matrices, ill-suited to low-precision,…
We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…
Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix.…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…
Sparse variational Gaussian process (SVGP) methods are a common choice for non-conjugate Gaussian process inference because of their computational benefits. In this paper, we improve their computational efficiency by using a dual…
Choosing a proper set of kernel functions is an important problem in learning Gaussian Process (GP) models since each kernel structure has different model complexity and data fitness. Recently, automatic kernel composition methods provide…
This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…
Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models…
Inference in Gaussian process (GP) models is computationally challenging for large data, and often difficult to approximate with a small number of inducing points. We explore an alternative approximation that employs stochastic inference…
Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…