Related papers: Testing Dependency of Weighted Random Graphs
We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated…
Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…
Randomness or mutual independence is a fundamental assumption forming the basis of statistical inference across disciplines such as economics, finance, and management. Consequently, validating this assumption is essential for the reliable…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated;…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
In this paper, we consider the hypothesis testing of correlation between two $m$-uniform hypergraphs on $n$ unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperdges…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
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…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
Graph data has a unique structure that deviates from standard data assumptions, often necessitating modifications to existing methods or the development of new ones to ensure valid statistical analysis. In this paper, we explore the notion…
Randomness or mutual independence is an important underlying assumption for most widely used statistical methods for circular data. Verifying this assumption is essential to ensure the validity and reliability of the resulting inferences.…
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 consider random graphs in which the edges are allowed to be dependent. In our model the edge dependence is quite general, we call it $p$-robust random graph. It means that every edge is present with probability at least $p$, regardless…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
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…
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality…