Related papers: On Discrete Gibbs Measure Approximation to Runs
A first order trace formula is obtained for a regular differential operator perturbed by a finite signed measure multiplication operator.
We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density $p(x)$…
In this paper, we have given a corrigendum to our paper "Some Approximation Results by $(p,q)$-analogue of Bernstein-Stancu Operators" published in Applied Mathematics and Computation $264 (2015) 392-402.$ We introduce a new analogue of…
Reliable robotic manipulation requires control policies that can accurately represent and adapt to uncertainty arising from contact-rich interactions. Modern data-driven methods mitigate uncertainty through large-scale training and…
We study the accuracy of a scaled Poisson approximation to the weighted sum of independent Poisson random variables, focusing on in particular the relative error of the tail distribution. A bound on the relative approximation error is…
This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These snapshots may represent densities of particles. The Wasserstein metric is…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of…
This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it…
The Gibbs Mixing Paradox is a conceptual touchstone for understanding mixtures in statistical mechanics. While debates over the theoretical subtleties of particle distinguishability continue to this day, we seek to extend the discussion in…
Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-R\"ollin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
The notion of Gibbs Measure is used by many researchers of the communities of Mathematical Physics, Probability, Thermodynamic Formalism, Symbolic Dynamics, and others. A natural question is when these several different notions of Gibbs…
We show, that under natural assumptions, solutions of Dirichlet problems for uniformly elliptic divergence form operator can be approximated pointwise by solutions of some versions of Robin problems. The proof is based on stochastic…
A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
We develop the tools necessary to use Stein's method for approximation by a Borel distribution, which we illustrate by considering the approximation of the number of customers served in the busy period of an M/G/1 queue. We further derive…
The present paper describes the experimental implementation of a measuring technique employing a slowly moving, near resonant, optical standing wave in the context of trapped ions. It is used to measure several figures of merit that are…