Related papers: Efficient reduced-rank methods for Gaussian proces…

Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…

We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…

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…

In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…

We describe randomized algorithms for computing the dominant eigenmodes of the Generalized Hermitian Eigenvalue Problem (GHEP) $Ax=\lambda Bx$, with $A$ Hermitian and $B$ Hermitian and positive definite. The algorithms we describe only…

Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions…

We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are…

Gaussian processes~(Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization…

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRF) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods,…

We introduce a stochastic variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in…

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

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…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…

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…

Bayesian optimization with Gaussian process as surrogate model has been successfully applied to analog circuit synthesis. In the traditional Gaussian process regression model, the kernel functions are defined explicitly. The computational…

In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based models such as SVM is, that the…

Gaussian Process (GP) regression is a popular and sample-efficient approach for many engineering applications, where observations are expensive to acquire, and is also a central ingredient of Bayesian optimization (BO), a highly prevailing…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…