arXiv research

The NNGP kernel's predictions closely match those of the Matern kernel under certain conditions.

Paper speeds up Gaussian process inference using Matérn kernels.

The paper explores the identifiability and interpretability of Gaussian process models using different kernel structures.

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

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

Optimizes Gaussian process hyperparameters using Bayesian autoregression.

Study finds polynomial convergence rate for Farey sequences linked to Riemann hypothesis.

Exact and scalable algorithm for Gaussian process regression with Matérn correlations.

We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter $ν$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $π$-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $ν>1…

New random feature maps for Laplacian and related kernels.

GP-UCB resolves sublinear regret for kernelized bandits.

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…

Proposes a new model for traffic flow on directed graphs.

cvHM framework speeds up GP inference for neural spike train analysis.

Develops kernels for matchings, overcoming computational challenges.

Standard Gaussian Process outperforms in high-dimensional Bayesian Optimization.

The paper establishes bounds on the smoothness parameter in Gaussian process interpolation.

New Gaussian processes for Riemannian manifolds enable uncertainty quantification.

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

Paper analyzes consistency of Bayesian and machine learning methods for hierarchical parameter estimation.

New RL method handles large state-action spaces with complex models.

We develop Fourier methods to expand translation-invariant kernels.

Adaptive RBF-KAN improves KANs by dynamically adjusting kernel parameters.

Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.

The paper improves bounds on regret in Gaussian process bandits.

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

A new kernel improves Gaussian process performance for non-stationary data.

CEI achieves convergence rates for constrained Bayesian optimization.

There is a need for affordable, widely deployable maternal-fetal ECG monitors to improve maternal and fetal health during pregnancy and delivery. Based on the diffusion-based channel selection, here we present the mathematical formalism and clinical validation of an algorithm capable of accurate separation of maternal …

Standard kernels such as Matérn or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more complicated patterns in the data. Spectral mixture kernels have recently been generalized in…

New algorithm improves Gaussian process hyperparameter tuning for large datasets.

Improved kernel ridge regression for large datasets using weighted random binning.

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial data, treating and discovering unknown equation parameters as hyperparameters of a…

The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses e…

Graph Gaussian processes use Matérn models for better function learning.

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

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distri…

Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds

Improves probability distribution compression with KT algorithm.

A new method estimates multi-dimensional value distributions using Hilbert space embeddings.

The multiple fundamental frequency detection problem and the source separation problem from a single-channel signal containing multiple oscillatory components and a nonstationary noise are both challenging tasks. To extract the fetal electrocardiogram (ECG) from a single-lead maternal abdominal ECG, we face both challe…

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

In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of semi-inner-products, we can obtain the explicit representations of the dual (nor…

The paper defines conditions for Gaussian process sample path regularity.

Unified kernels for diverse applications in math and stats.

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 black box optimization of an unknown function in the nonparametric Gaussian process setting when the noise in the observed function values can be heavy tailed. This is in contrast to existing literature that typically assumes sub-Gaussian noise distributions for queries. Under the assumption that the unknow…

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