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The $\beta$-model has been extensively utilized to model degree heterogeneity in networks, wherein each node is assigned a unique parameter. In this article, we consider the hypothesis testing problem that two nodes $i$ and $j$ of a…

Statistics Theory · Mathematics 2024-03-12 Kang Fu , Jianwei Hu , Meng Sun

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…

Combinatorics · Mathematics 2020-08-12 Carlos Hoppen , Yoshiharu Kohayakawa , Richard Lang , Hanno Lefmann , Henrique Stagni

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…

Signal Processing · Electrical Eng. & Systems 2024-09-09 Rishabh Ravi , Kaushani Majumder , Kalp Vyas , Satish Mulleti

The graph similarity problem, also known as approximate graph isomorphism or graph matching problem, has been extensively studied in the machine learning community, but has not received much attention in the algorithms community: Given two…

Data Structures and Algorithms · Computer Science 2018-02-26 Martin Grohe , Gaurav Rattan , Gerhard J. Woeginger

We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks,…

Statistics Theory · Mathematics 2017-10-24 Hamid Javadi , Andrea Montanari

How can researchers test for heterogeneity in the local structure of a network? In this paper, we present a framework that utilizes random sampling to give subgraphs which are then used in a goodness of fit test to test for heterogeneity.…

Methodology · Statistics 2015-12-04 Jonathan Tuke , Matthew Roughan

We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…

Machine Learning · Computer Science 2020-12-03 Romuald A. Janik , Aleksandra Nowak

Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…

Methodology · Statistics 2024-05-08 M. V. Alba-Fernández , M. D. Jiménez--Gamero , F. J. Ariza-López

We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…

Probability · Mathematics 2012-10-25 Luc Devroye , Nicolas Fraiman

The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…

Information Theory · Computer Science 2016-04-18 Dayu Huang , Sean Meyn

For a fixed graph $H$ and for arbitrarily large host graphs $G$, the number of homomorphisms from $H$ to $G$ and the number of subgraphs isomorphic to $H$ contained in $G$ have been extensively studied in extremal graph theory and graph…

Combinatorics · Mathematics 2021-07-05 Chun-Hung Liu

The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…

Quantum Physics · Physics 2026-03-31 Prateek P. Kulkarni

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

Combinatorics · Mathematics 2025-08-08 Catherine Greenhill

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

Methodology · Statistics 2024-02-05 Meijia Shao , Dong Xia , Yuan Zhang , Qiong Wu , Shuo Chen

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

Statistics Theory · Mathematics 2020-06-01 Rémy Mariétan , Stephan Morgenthaler

This paper is concerned with the testing bilateral linear hypothesis on the mean matrix in the context of the generalized multivariate analysis of variance (GMANOVA) model when the dimensions of the observed vector may exceed the sample…

Methodology · Statistics 2024-04-04 Takayuki Yamada , Tetsuto Himeno , Annika Tillander , Tatjana Pavlenko

Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…

Methodology · Statistics 2019-11-19 Ilmun Kim , Ann B. Lee , Jing Lei

Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…

Information Theory · Computer Science 2020-08-24 B. Subbareddy , Aditya Siripuram , Jingxin Zhang

Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…

The graph isomorphism problem is considered. We assign modified $n$-variable characteristic polynomials for graphs and reduce the graph isomorphism problem to the problem of the polynomials isomorphism. It is required to find out, is there…

Discrete Mathematics · Computer Science 2024-10-18 Alexander Prolubnikov