Related papers: Small deviations for a family of smooth Gaussian p…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…

Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 large deviation {\em functional} characterizing the empirical density of the underlying…

This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…

A fully discrete Lagrangian scheme for solving a family of fourth order equations numerically is presented. The discretization is based on the equation's underlying gradient flow structure w.r.t. the $L^2$-Wasserstein distance, and adapts…

Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted function values. For the quantified uncertainties to be…

We investigate unbiased high-dimensional mean estimators in differential privacy. We consider differentially private mechanisms whose expected output equals the mean of the input dataset, for every dataset drawn from a fixed bounded…

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…

Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…

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…

We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…

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…

Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer science, and learning theory. In this paper, we consider centered…

This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…

This paper is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly-symmetric stationary…

In this paper, we propose a method to approximate the Gaussian function on ${\mathbb R}$ by a short cosine sum. We generalise and extend the differential approximation method proposed in [4, 40] to approximate $\mathrm{e}^{-t^{2}/2\sigma}$…

We introduce a new method for analyzing midpoint discretizations of stochastic differential equations (SDEs), which are frequently used in Markov chain Monte Carlo (MCMC) methods for sampling from a target measure $\pi \propto \exp(-V)$.…