arXiv research

Paper evaluates squared-exponential covariance function for Gaussian processes with integral observations.

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 covariance function should be adapted to the modeled data. Frequently, the squared expo…

New GP kernels avoid mean reversion without losing smoothness.

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…

We study the average case performance of multi-task Gaussian process (GP) regression as captured in the learning curve, i.e. the average Bayes error for a chosen task versus the total number of examples $n$ for all tasks. For GP covariances that are the product of an input-dependent covariance function and a free-form …

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of $\mathbb{R}^d$. On this approximate eigenbasis the eigenvalues of the c…

New method reduces computational cost of Gaussian process regression.

The study examines numerical aspects of Karhunen-Loève expansions for stochastic processes.

Deep Gaussian Processes are reinterpreted as deep trigonometric networks for tractable inference.

Polynomial-time algorithm estimates edge density of random graphs with privacy and robustness.

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…

New Hida-Matérn kernels enable flexible process priors and efficient GP inference.

The paper explores a new type of kernel using Wasserstein distance for better classification of shapes.

Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.

The paper improves error bounds for Bayesian quadrature in noisy settings.

Paper establishes no-regret property for practical EGO optimization.

Improved Gaussian process approximations reduce computational cost.

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order interactions. However, until recently, there has been a strong reliance on a limi…

We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…

Let $\mathcal T$ be the Teichmüller space of marked genus $g$, $n$ punctured Riemann surfaces with its bordification $\Tbar$ the {\em augmented Teichmüller space} of marked Riemann surfaces with nodes, \cite{Abdegn, Bersdeg}. Provided with the WP metric $\Tbar$ is a complete CAT(0) metric space, \cite{DW2, Wlcomp, Yam2…

Polynomial-time algorithm estimates mean with bounded covariance using differential privacy.

This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.

Researchers use Gaussian processes with non-stationary kernels to model precipitation patterns in the Upper Indus Basin.

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-expo…

We consider the problem of Bayesian optimization (BO) in one dimension, under a Gaussian process prior and Gaussian sampling noise. We provide a theoretical analysis showing that, under fairly mild technical assumptions on the kernel, the best possible cumulative regret up to time $T$ behaves as $Ω(\sqrt{T})$ and $O(\s…

New analysis explains pathology of deep Gaussian processes.

We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be approximated by a grid and when correlations among data are short-ranged, the kernel matrix…

A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different datasets through model composition, enhance predictions of quantities of interest thr…

The paper analyzes the statistical cost of tuning kernel hyperparameters in robust regression.

A scalable framework for inference in continuous Cox processes using Gaussian processes.

New Gaussian processes for Riemannian manifolds enable uncertainty quantification.

GPs' decisions can vary significantly with different kernels, even if kernels are qualitatively similar.

Paper tackles non-stationary kernelized bandits with near-optimal algorithm.

We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the model using a latent marked Poisson process and Pólya--Gamma random variables w…

Deep-HGP uses Bayesian nonparametric approach for complex data regression.

A new method uses Gaussian Processes for feature-based nonrigid image registration.

New Fourier features improve high-precision approximation in large-scale problems.

Proposes Gaussian process priors on graph sets with geometric structure.

CEI achieves convergence rates for constrained Bayesian optimization.

The paper analyzes convergence rates of Gaussian process approximations for scalable regression.

Optimistic algorithm reduces regret in non-stationary linear MDPs.

In this paper, we consider the problem of sequentially optimizing a black-box function $f$ based on noisy samples and bandit feedback. We assume that $f$ is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yielding a commonly-considered non-Bayesian form of Gaussian process …

Bayesian optimization under heavy-tailed noise with improved regret bounds.

The paper analyzes how Gaussian kernel parameters affect posterior covariance in Gaussian processes.

A batched Gaussian Process bandit optimization method achieves near-optimal regret bounds.

CovRegRF estimates covariance matrix from covariates using random forests.

Unified analysis of Gaussian Process Thompson Sampling without discretization.

Privacy improves robustness in statistical estimation.