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Rate-Distortion Function of the Stochastic Block Model
- Publication Year :
- 2023
-
Abstract
- The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the Erd\H{o}s-R\'enyi (ER) random graph model.<br />Comment: 9 pages, 1 figure, Accepted for presentation at Asilomar Conference on Signals, Systems, and Computers, 2023
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2309.14464
- Document Type :
- Working Paper