Related papers: Moment kernels, nested defects, and Cuntz dilation…
In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…
We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal…
Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…
We show that a formal power series in $2N$ non-commuting indeterminates is a positive non-commutative kernel if and only if the kernel on $N$-tuples of matrices of any size obtained from this series by matrix substitution is positive. We…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
For a class of $O(n+1,R)$ invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the reproducing kernels of the associated Bergman spaces, discuss the corresponding asymptotic expansions of…
We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler…
We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly…
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
The formation of topological defects during continuous second-order phase transitions is well described by the Kibble-Zurek mechanism (KZM). However, when the spontaneously broken symmetry is only approximate, such transitions become smooth…
This paper investigates weak convergence of U-statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U-statistic exists is relaxed to having 4/3 moments only (modulo a…
Change-points in time series data are usually defined as the time instants at which changes in their properties occur. Detecting change-points is critical in a number of applications as diverse as detecting credit card and insurance frauds,…
The complete positivity, i.e., positivity of the resolvent kernels, for convolutional kernels is an important property for the positivity property and asymptotic behaviors of Volterra equations. We inverstigate the discrete analogue of the…
Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects are represented and on the distribution assumed on these…
We present the formalism for consistently transforming transition operators within the in-medium similarity renormalization group framework. We implement the operator transformation in both the equations-of-motion and valence-space…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…
Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the…
A uniform in probability approximation is established for Studentized processes of non degenerate U-statistics of order m greater or equal to 2 in terms of a standard Wiener process. The classical condition that the second moment of kernel…
We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain…