Related papers: Provably Reliable Large-Scale Sampling from Gaussi…

We investigate the ability to reconstruct and derive spatial structure from sparsely sampled 3D piezoresponse force microcopy data, captured using the band-excitation (BE) technique, via Gaussian Process (GP) methods. Even for weakly…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations…

Given a dataset of $n$ i.i.d. samples from an unknown distribution $P$, we consider the problem of generating a sample from a distribution that is close to $P$ in total variation distance, under the constraint of differential privacy (DP).…

In geostatistical problems with massive sample size, Gaussian processes can be approximated using sparse directed acyclic graphs to achieve scalable $O(n)$ computational complexity. In these models, data at each location are typically…

One obstacle to the use of Gaussian processes (GPs) in large-scale problems, and as a component in deep learning system, is the need for bespoke derivations and implementations for small variations in the model or inference. In order to…

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 provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…

Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models,…

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…

The transduction of sequence has been mostly done by recurrent networks, which are computationally demanding and often underestimate uncertainty severely. We propose a computationally efficient attention-based network combined with the…

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…

Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…

Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient…

Studies of hadron resonances and their properties are limited by the accuracy and consistency of measured datasets, which can originate from many different experiments. We have used Gaussian Processes (GP) to build interpolated datasets,…

Thompson Sampling (TS) from Gaussian Process (GP) models is a powerful tool for the optimization of black-box functions. Although TS enjoys strong theoretical guarantees and convincing empirical performance, it incurs a large computational…

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…