# Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence

@article{Jog2015InformationtheoreticBF, title={Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence}, author={Varun Jog and Po-Ling Loh}, journal={ArXiv}, year={2015}, volume={abs/1509.06418} }

We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a distribution determined by the community membership of its endpoints. Our main result, characterizing the precise boundary between success and failure of maximum likelihood estimation when edge weights are drawn from discrete distributions, involves the Renyi…

## 51 Citations

Recovering communities in weighted stochastic block models

- Computer Science2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2015

We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each…

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This paper develops a polynomial-time two-stage algorithm that meets the threshold of exact recovery in the general d-uniform hypergraph stochastic block model and recovers prior results for the standard SBM and d-HSBM with two symmetric communities as special cases.

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A class of adaptive tests that are computationally tractable and completely data-driven that achieve nontrivial powers in the contiguous regime and consistency in the singular regime whenever $n p_{n,av} \to\infty$ is the average connection probability.

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- Computer Science, Mathematics2019 IEEE International Symposium on Information Theory (ISIT)
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A new toy model for planted generative models called planted Random Energy Model (REM), inspired by Derrida’s REM is proposed, which provides the asymptotic behaviour of the probability of error for the maximum likelihood estimator and hence the exact recovery threshold.

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- Computer Science
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A weighted generalization of the stochastic block models, in which observations are collected in the form of a weighted adjacency matrix and the weight of each edge is generated independently from an unknown probability density determined by the community membership of its endpoints, is studied.

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- Computer ScienceJ. Mach. Learn. Res.
- 2017

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- 2016

The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to statistical and computational tradeoffs, and for various recovery requirements such as exact, partial and weak recovery.

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- Computer ScienceArXiv
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The paper proves the efficient detection to non-symmetrical SBMs with a generalized notion of detection and KS threshold, and connects ABP to a power iteration method with a nonbacktracking operator of generalized order, formalizing the interplay between message passing and spectral methods.

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The optimal sample complexity is analyzed and different regimes whose characteristics rely on quality metrics of side information of the hierarchical similarity graph are identified and it is shown that the characterized information-theoretic limit can be asymptotically achieved.

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