Related papers: Quantum mixing of Markov chains for special distri…
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…
Using elementary methods, we prove that for a countable Markov chain $P$ of ergodic degree $d > 0$ the rate of convergence towards the stationary distribution is subgeometric of order $n^{-d}$, provided the initial distribution satisfies…
A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
We study a simple Markov chain, the switch chain, on the set of all perfect matchings in a bipartite graph. This Markov chain was proposed by Diaconis, Graham and Holmes as a possible approach to a sampling problem arising in Statistics. We…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
In network modeling of complex systems one is often required to sample random realizations of networks that obey a given set of constraints, usually in form of graph measures. A much studied class of problems targets uniform sampling of…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter $\ep$. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge…
We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous time Markov chains. Here we present a class of models that appears…
Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
Most approximation algorithms for #P-complete problems (e.g., evaluating the permanent of a matrix or the volume of a polytope) work by reduction to the problem of approximate sampling from a distribution $\pi$ over a large set $\S$. This…