Testing Dependency of Weighted Random Graphs

Autor:	Oren, Mor, Paslev, Vered, Huleihel, Wasim
Rok vydání:	2024
Předmět:	Computer Science - Machine Learning Computer Science - Information Theory
Druh dokumentu:	Working Paper
Popis:	In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically independent, whereas under the alternative, the edges of one graph are dependent on the edges of a uniformly and randomly vertex-permuted version of the other graph. For general edge-weight distributions, we establish thresholds at which optimal testing becomes information-theoretically possible or impossible, as a function of the total number of nodes in the observed graphs and the generative distributions of the weights. Finally, we identify a statistical-computational gap, and present evidence suggesting that this gap is inherent using the framework of low-degree polynomials. Comment: 32 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.14870 Zobrazit plný text záznamu View this record from Arxiv