Related papers: Metrizing Weak Convergence with Maximum Mean Discr…

Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…

In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…

We study posterior contraction rates for mixing measures in homoscedastic location-scale mixture models with infinitely many components. While posterior convergence at the level of densities is well understood, ensuring convergence of the…

This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…

We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then…

This paper establishes error bounds for the convergence of a piecewise linear approximation of the constrained optimal smoothing problem posed in a reproducing kernel Hilbert space (RKHS). This problem can be reformulated as a Bayesian…

Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is…

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

It is known that the space of boundedly finite integer-valued measures on a complete separable metric space becomes itself a complete separable metric space when endowed with the weak-hash metric. It is also known that convergence under…

We reprove the well known fact that the energy distance defines a metric on the space of Borel probability measures on a Hilbert space with finite first moment by a new approach, by analyzing the behavior of the Gaussian kernel on Hilbert…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in…

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

In this note we study a natural measure on plane partitions giving rise to a certain discrete-time Muttalib-Borodin process (MBP): each time-slice is a discrete version of a Muttalib-Borodin ensemble (MBE). The process is determinantal with…

In this study, we establish a basis for selecting similarity measures when applying machine learning techniques to solve materials science problems. This selection is considered with an emphasis on the distinctiveness between materials that…

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels $K(x,y) = - \|x-y\|^r$, $r \in (0,2)$ have exceptional properties which allow…

The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are…

We study equivalent descriptions of the vague, weak, setwise and total-variation (TV) convergence of sequences of Borel measures on metrizable and non-metrizable topological spaces in this work. On metrizable spaces, we give some equivalent…