Related papers: A Cycle Walk for Sampling Measures on Spanning For…
The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…
We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…
This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…
A crucial task in the political redistricting problem is to sample redistricting plans i.e. a partitioning of the graph of census blocks into districts. We show that Recombination [DeFord-Duchin-Solomon'21]-a popular Markov chain to sample…
Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…
Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…
Given random walk on a graph, the corresponding discrete-time quantum walk can be constructed using the method proposed by Szegedy. On the other hand, given a partition of the set of states of a Markov chain, one can study the corresponding…
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…
This work considers the general task of estimating the sum of a bounded function over the edges of a graph, given neighborhood query access and where access to the entire network is prohibitively expensive. To estimate this sum, prior work…
We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…
Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…
We exhibit a one to one correspondence between some universal probabilistic properties of the ordering coordinate of one-dimensional Ising-like models and a class of continuous time random walks. This correspondence provides an new…
The gerrymandering problem is a worldwide problem which sets great threat to democracy and justice in district based elections. Thanks to partisan redistricting commissions, district boundaries are often manipulated to benefit incumbents.…
Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…