Related papers: An approximation theory for Markov chain compressi…
The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating…
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by "controlled" Markov noise. In particular, the faster and slower recursions have non-additive controlled Markov noise…
The Krylov subspace method is a standard approach to approximate quantum evolution, allowing to treat systems with large Hilbert spaces. Although its application is general, and suitable for many-body systems, estimation of the committed…
This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large finite state space or a countably infinite state space. The…
This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber…
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently…
In distribution compression, one aims to accurately summarize a probability distribution $\mathbb{P}$ using a small number of representative points. Near-optimal thinning procedures achieve this goal by sampling $n$ points from a Markov…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
In the paper, the approximate sequence for entropy of some binary hidden Markov models has been found to have two bound sequences, the low bound sequence and the upper bound sequence. The error bias of the approximate sequence is bound by a…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of conservation law equations is proposed. This framework allows…
Parameter reduction has been an important topic in deep learning due to the ever-increasing size of deep neural network models and the need to train and run them on resource limited machines. Despite many efforts in this area, there were no…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
The paper is concerned with the approximation of the deterministic the mean field type control system by a mean field Markov chain. It turns out that the dynamics of the distribution in the approximating system is described by a system of…
This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded…
We consider the problem of estimating the measure of subsets in very large networks. A prime tool for this purpose is the Markov Chain Monte Carlo (MCMC) algorithm. This algorithm, while extremely useful in many cases, still often suffers…
The paper is concerned with approximating the distribution of a sum W of n integer valued random variables Y_i, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a…