Related papers: Detecting Correlation between Multiple Unlabeled G…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
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…
Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…
We determine an asymptotic formula for the number of labelled 2-connected (simple) graphs on $n$ vertices and $m$ edges, provided that $m-n\to\infty$ and $m=O(n\log n)$ as $n\to\infty$. This is the entire range of $m$ not covered by…
A sequential test is proposed for detection and isolation of hubs in a correlation graph. Hubs in a correlation graph of a random vector are variables (nodes) that have a strong correlation edge. It is assumed that the random vectors are…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
In this paper, we investigate the problem of deciding whether two standard normal random vectors $\mathsf{X}\in\mathbb{R}^{n}$ and $\mathsf{Y}\in\mathbb{R}^{n}$ are correlated or not. This is formulated as a hypothesis testing problem,…
Pairwise network models such as the Gaussian Graphical Model (GGM) are a powerful and intuitive way to analyze dependencies in multivariate data. A key assumption of the GGM is that each pairwise interaction is independent of the values of…
Link sign prediction on a signed graph is a task to determine whether the relationship represented by an edge is positive or negative. Since the presence of negative edges violates the graph homophily assumption that adjacent nodes are…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…
Emerging applications of sensor networks for detection sometimes suggest that classical problems ought be revisited under new assumptions. This is the case of binary hypothesis testing with independent - but not necessarily identically…
We study the problem of testing the existence of a heterogeneous dense subhypergraph. The null hypothesis corresponds to a heterogeneous Erd\"{o}s-R\'{e}nyi uniform random hypergraph and the alternative hypothesis corresponds to a…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
Let $G$ be a simple connected graph on $n$ vertices and $m$ edges. In [Linear Algebra Appl. 435 (2011) 2570-2584], Lima et al. posed the following conjecture on the least eigenvalue $q_n(G)$ of the signless Laplacian of $G$: $\displaystyle…
The Gaussian graphical model (GGM) has become a popular tool for analyzing networks of psychological variables. In a recent paper in this journal, Forbes, Wright, Markon, and Krueger (FWMK) voiced the concern that GGMs that are estimated…
Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…
Identifying differences in networks has become a canonical problem in many biological applications. Here, we focus on testing whether two Gaussian graphical models are the same. Existing methods try to accomplish this goal by either…
In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well…