Related papers: Couplings of the Random-Walk Metropolis algorithm
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
This paper explores decentralized learning in a graph-based setting, where data is distributed across nodes. We investigate a decentralized SGD algorithm that utilizes a random walk to update a global model based on local data. Our focus is…
It is common practice in Markov chain Monte Carlo to update the simulation one variable (or sub-block of variables) at a time, rather than conduct a single full-dimensional update. When it is possible to draw from each full-conditional…
In [4], we examined the use of coupling to obtain bounds on the mixing time of statistics on Markov chains. In the present paper, we consider the same general problem, but using strong stationary times rather than coupling. We discuss…
Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…
This paper explores the mixing time of the random transposition walk on the symmetric group. While it has long been known that this walk mixes in order n*log(n) time, this result has not previously been attained using coupling. A coupling…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
We construct a new Markov chain Monte Carlo method on finite states with optimal choices of acceptance-rejection ratio functions. We prove that the constructed continuous time Markov jumping process has a global in-time convergence rate in…
Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
The choice of the increment distribution is crucial for the random-walk Metropolis-Hastings (RWM) algorithm. In this paper we study the optimal choice in high-dimension setting among all possible increment distributions. The conclusion is…
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…