Related papers: Convergence rate bounds for iterative random funct…
The problem of efficiently sampling from a set of (undirected, or directed) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the…
Simulated tempering is a widely used strategy for sampling from multimodal distributions. In this paper, we consider simulated tempering combined with an arbitrary local Markov chain Monte Carlo sampler and present a new decomposition…
The switching model is a Markov chain approach to sample graphs with fixed degree sequence uniformly at random. The recently invented Curveball algorithm for bipartite graphs applies several switches simultaneously (`trades'). Here, we…
This paper presents a self-contained account for coupling arguments and applications in the context of Markov processes. We first use coupling to describe the transport problem, which leads to the concepts of optimal coupling and…
This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased…
In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove…
In recent work of Baik, Deift and Rains convergence of moments was established for the limiting joint distribution of the lengths of the first k rows in random Young tableaux. The main difficulty was obtaining a good estimate for the tail…
One-shot information theory addresses scenarios in source coding and channel coding where the signal blocklength is assumed to be 1. In this case, each source and channel can be used only once, and the sources and channels are arbitrary and…
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…
The Curveball algorithm is a variation on well-known switch-based Markov chain approaches for uniformly sampling binary matrices with fixed row and column sums. Instead of a switch, the Curveball algorithm performs a so-called binomial…
This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a…
The Markov chain approximation of a one-dimensional symmetric diffusion is investigated in this paper. Given an irreducible reflecting diffusion on a closed interval with scale function $s$ and speed measure $m$, the approximating Markov…
A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the…
In a model of communication in a social network described by a simple consensus model, we pose the problem of finding a subset of nodes with given cardinality and fixed consensus values that enable the fastest convergence rate to…
We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the computational cost of interacting particle systems. We construct…
One-shot achievable rate region for source coding when coded side information is available at the decoder (source coding with a helper) is proposed. The achievable region proposed is in terms of conditional smooth max Renyi entropy and…
We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic…
We apply the method of differential inequalities for the computation of upper bounds for the rate of convergence to the limiting regime for one specific class of (in)homogeneous continuous-time Markov chains. To obtain these estimates, we…
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…