Related papers: Hypothesis testing for the uniformity of random ge…
Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding…
Connectivity is one of the most fundamental properties of wireless multi-hop networks. A network is said to be connected if there is a path between any pair of nodes. A convenient way to study the connectivity of a random network is by…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding $p$-value. The goal is to make…
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…
Consider a connected graph $G=(E,V)$ with $N=|V|$ vertices. The main purpose of this paper is to explore the question of uniform sampling of a subtree of $G$ with $n$ nodes, for some $n\leq N$ (the spanning tree case correspond to $n=N$,…
Graph (or network) is a mathematical structure that has been widely used to model relational data. As real-world systems get more complex, multilayer (or multiple) networks are employed to represent diverse patterns of relationships among…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
We study the problem of testing the existence of a dense subhypergraph. The null hypothesis is an Erdos-Renyi uniform random hypergraph and the alternative hypothesis is a uniform random hypergraph that contains a dense subhypergraph. We…
Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following…
We consider properties of edge-colored vertex-ordered graphs, i.e., graphs with a totally ordered vertex set and a finite set of possible edge colors. We show that any hereditary property of such graphs is strongly testable, i.e., testable…
A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that…
Given a class $\mathcal G$ of graphs, let ${\mathcal G}_n$ denote the set of graphs in $\mathcal G$ on vertex set $[n]$. For certain classes $\mathcal G$, we are interested in the asymptotic behaviour of a random graph $R_n$ sampled…
One of the intensely studied concepts of network robustness is $r$-robustness, which is a network topology property quantified by an integer $r$. It is required by mean subsequence reduced (MSR) algorithms and their variants to achieve…
We initiate a thorough study of \emph{distributed property testing} -- producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called \emph{dense} testing model we emulate…
Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…
Random intersection graphs have received much attention for nearly two decades, and currently have a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. In this paper, we…
Motivated by gene set enrichment analysis, we investigate the problem of combined hypothesis testing on a graph. We introduce a general framework to effectively use the structural information of the underlying graph when testing…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…