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arXiv · 2309.14464

Rate-Distortion Function of the Stochastic Block Model

Martin Wachiye Wafula·Praneeth Kumar Vippathalla·Justin Coon·Mihai-Alin Badiu
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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.

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Martin Wachiye Wafula, Praneeth Kumar Vippathalla, Justin Coon, Mihai-Alin Badiu. 2023-09-25. Rate-Distortion Function of the Stochastic Block Model. https://arxiv.org/abs/2309.14464

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