Related papers: Operator-free Equilibrium on the Sphere
Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_2$ on a usual compact space $\mathcal M$, Gr\"ochenig introduced the weighted least squares polynomials and the least squares quadrature from pointwise samples of a function, and…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…
A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing…
Distributional comparison is a fundamental problem in statistical data analysis with numerous applications in a variety of scientific and engineering fields. Numerous methods exist for distributional comparison but kernel Stein's method has…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
Universality, namely distributional invariance, is a well-known property for many random structures. For example, it is known to hold for a broad range of variational problems with random input. Much less is known about the algorithmic…
The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for…
As a new technique it is shown how general pseudo-differential operators can be estimated at arbitrary points in Euclidean space when acting on functions $u$ with compact spectra. The estimate is a factorisation inequality, in which one…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…
We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…
The seminal 2009 paper by Bernard, Krauth, and Wilson marked a paradigm shift in Monte Carlo sampling. By abandoning the restrictive condition of detailed balance in favor of the more fundamental principle of global balance, they introduced…
The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…
Planetary ephemerides are a very powerful tool to constrain deviations from the theory of General Relativity using orbital dynamics. The effective field theory framework called the Standard-Model Extension (SME) has been developed in order…
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a…
In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…