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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…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gaussian processes (GPs) are a mature and widely-used component of the ML toolbox. One of their desirable qualities is automatic hyperparameter selection, which allows for training without user intervention. However, in many realistic…
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,…
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…
We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not…
Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification. In this paper, we develop a method for comparing how close different generative…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
We present a planning framework for minimising the deterministic worst-case error in sparse Gaussian process (GP) regression. We first derive a universal worst-case error bound for sparse GP regression with bounded noise using interpolation…
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure…
Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution…
Consider the sequential optimization of an expensive to evaluate and possibly non-convex objective function $f$ from noisy feedback, that can be considered as a continuum-armed bandit problem. Upper bounds on the regret performance of…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets…
In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…