Related papers: Integration in reproducing kernel Hilbert spaces o…
Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…
3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…
In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance…
We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing…
Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al.…
The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space…
In this paper we first identify a basic limitation in gradient descent-based optimization methods when used in conjunctions with smooth kernels. An analysis based on the spectral properties of the kernel demonstrates that only a vanishingly…
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…
The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
This paper studies the optimality of kernel methods in high-dimensional data clustering. Recent works have studied the large sample performance of kernel clustering in the high-dimensional regime, where Euclidean distance becomes less…
This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace.…
One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…
This note responds to "Promises and Pitfalls of Deep Kernel Learning" (Ober et al., 2021). The marginal likelihood of a Gaussian process can be compartmentalized into a data fit term and a complexity penalty. Ober et al. (2021) shows that…