Related papers: Stein's method of exchangeable pairs in multivaria…
We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a…
We derive a new result for exponential approximation using Stein's method of exchangeable pairs. As an application, an exponential limit theorem with error term is derived for |Tr(U)|^2, where Tr(U) denotes the trace of a matrix chosen from…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…
The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the…
We propose a new version of Stein's method of exchangeable pairs, which, given a suitable exchangeable pair $(W,W')$ of real-valued random variables, suggests the approximation of the law of $W$ by a suitable absolutely continuous…
We propose a way of finding a Stein type characterization of a given absolutely continuous distribution $\mu$ on $\R$ which is motivated by a regression property satisfied by an exchangeable pair $(W,W')$ where $\calL(W)$ is supposed or…
We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by…
This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general…
Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…
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.…
Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order…
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…
This article derives quantitative limit theorems for multivariate Poisson and Poisson process approximations. Employing the solution of Stein's equation for Poisson random variables, we obtain an explicit bound for the multivariate Poisson…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our results generalize and refine the main…
The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…