Related papers: On the optimality of Stein factors
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
A general theory of stochastic decision forests is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional…
Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise…
We develop Stein's method for $\alpha$-stable approximation with $\alpha\in(0,1]$, continuing the recent line of research by Xu \cite{lihu} and Chen, Nourdin and Xu \cite{C-N-X} in the case $\alpha\in(1,2).$ The main results include an…
This article deals with Stein characterizations of probability distributions. We provide a general framework for interpreting these in terms of the parameters of the underlying distribution. In order to do so we introduce two concepts (a…
Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the…
We design a 3/2 approximation algorithm for the Generalized Steiner Tree problem (GST) in metrics with distances 1 and 2. This is the first polynomial time approximation algorithm for a wide class of non-geometric metric GST instances with…
We develop a new method for showing that a given sequence of random variables verifies an appropriate law of the iterated logarithm. Our tools involve the use of general estimates on multidimensional Wasserstein distances, that are in turn…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as…
A method to include multiplicative systematic uncertainties into branching ratio limits was proposed by M. Convery. That solution used approximations which are not necessarily valid. This note provides a solution without approximations and…
Exploiting Markoff's Theory for rational approximations of real numbers, we explicitly link how hard it is to approximate a given number to an idealized notion of growth capacity for plants which we express as a modular invariant function…
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
In this paper, we present a minimal formalism for Stein operators which leads to different probabilistic representations of solutions to Stein equations. These in turn provide a wide family of Stein-Covariance identities which we put to use…
In this paper, we analyze the periodic factors of Sturmian words for the findings to lead to a linear-time algorithm for the computation of runs in this class of words which, to our best knowledge, is an open problem in literature.
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…