Related papers: Empirical Sampling of Connected Graph Partitions f…
We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable…
We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear subject to a neighbourhood exclusion…
We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…
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…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require…
The mixer chain on a graph G is the following Markov chain. Place tiles on the vertices of G, each tile labeled by its corresponding vertex. A "mixer" moves randomly on the graph, at each step either moving to a randomly chosen neighbor, or…
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
Recently, an increasing number of researchers, especially in the realm of political redistricting, have proposed sampling-based techniques to generate a subset of plans from the vast space of districting plans. These techniques have been…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
Markov Chain Monte Carlo (MCMC) has been the de facto technique for sampling and inference of large graphs such as online social networks. At the heart of MCMC lies the ability to construct an ergodic Markov chain that attains any given…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
We develop effective methods for constructing an ensemble of district plans via independent sampling from a reasonable probability distribution on the space of graph partitions. We compare the performance of our algorithms to that of…
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they do…
Graph embedding maps a graph into a convenient vector-space representation for graph analysis and machine learning applications. Many graph embedding methods hinge on a sampling of context nodes based on random walks. However, random walks…