arXiv research

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

The paper analyzes expected improvement policies for minimizing functions in RKHSs and derives regret bounds.

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

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

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

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

Improved Gaussian process approximations reduce computational cost.

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…

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

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

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…

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

Bayesian optimization in one dimension achieves $O(\sqrt{T\log T})$ regret.

New analysis explains pathology of deep Gaussian processes.

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

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…

Improves spatial statistics with nonstationary kernels.

Unified analysis of kernel-based and locally adaptive bandit optimization methods.

SWD approximates GP for faster regression.

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…

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

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…

New GP kernels avoid mean reversion without losing smoothness.

GeometricKernels package implements kernels for uncertain data on graphs, manifolds, and meshes.

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

CEI achieves convergence rates for constrained Bayesian optimization.

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

Unified analysis of Gaussian Process Thompson Sampling without discretization.

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

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

Standard Gaussian Process outperforms in high-dimensional Bayesian Optimization.

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

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 …

BKTF uses tensor factorization for Bayesian optimization of complex functions.

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

Neural processes approximate Gaussian process inference, revealing three key costs.

Proposes Gaussian process priors on graph sets with geometric structure.

Paper establishes no-regret property for practical EGO optimization.

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 algorithm optimizes Hölder smooth functions in RKHS with tighter regret bounds.

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

New Gaussian processes for Riemannian manifolds enable uncertainty quantification.

Paper analyzes GP-EI for Bayesian optimization with no regret and provides guidance on choosing incumbents.

Bayesian Gaussian Process ODEs enhanced with normalizing flows for improved flexibility and accuracy.

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

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

Efficiently infers Poisson process intensity using Gaussian process with sigmoid link.

Optimistic algorithm reduces regret in non-stationary linear MDPs.