TY - GEN
T1 - Testing Dependency of Weighted Random Graphs
AU - Oren-Loberman, Mor
AU - Paslev, Vered
AU - Huleihel, Wasim
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - 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, while under the alternative, the edges of one graph are dependent on the edges of a randomly vertex-permuted version of the other graph. For general edge-weights distributions, we establish thresholds at which optimal testing is information-theoretically impossible and possible, as a function of the total number of nodes in the observed graphs and the generative distributions of the weights. Finally, we observe a statistical-computational gap in our problem, and we provide evidence that this is fundamental using the framework of low-degree polynomials.
AB - 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, while under the alternative, the edges of one graph are dependent on the edges of a randomly vertex-permuted version of the other graph. For general edge-weights distributions, we establish thresholds at which optimal testing is information-theoretically impossible and possible, as a function of the total number of nodes in the observed graphs and the generative distributions of the weights. Finally, we observe a statistical-computational gap in our problem, and we provide evidence that this is fundamental using the framework of low-degree polynomials.
UR - http://www.scopus.com/inward/record.url?scp=85202804006&partnerID=8YFLogxK
U2 - 10.1109/ISIT57864.2024.10619266
DO - 10.1109/ISIT57864.2024.10619266
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AN - SCOPUS:85202804006
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1263
EP - 1268
BT - 2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 IEEE International Symposium on Information Theory, ISIT 2024
Y2 - 7 July 2024 through 12 July 2024
ER -