# Belief propagation, robust reconstruction and optimal recovery of block models

@inproceedings{Mossel2014BeliefPR, title={Belief propagation, robust reconstruction and optimal recovery of block models}, author={Elchanan Mossel and Joe Neeman and Allan Sly}, booktitle={COLT}, year={2014} }

We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities a=n and b=n for inter- and intra-block edge probabilities respectively. It was recently shown that one can do better than a random guess if and only if (a b) 2 > 2(a + b). Using a variant of Belief Propagation, we give a reconstruction algorithm that is optimal in the sense that if (a b) 2 > C(a + b) for some constant C then our algorithm maximizes the fraction of the nodes…

## 157 Citations

### Optimal Reconstruction of General Sparse Stochastic Block Models

- Computer Science, Mathematics
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The main contribution of their proof is to show that when the signal to noise ratio is sufficiently large, in particular λd > C, the reconstruction accuracy on a tree with or without noise on the leaves is asymptotically the same.

### Optimal Recovery of Block Models with $q$ Communities

- Computer ScienceArXiv
- 2020

This paper will generalize the paper's results, including the main step, to any number of communities, providing an algorithm related to Belief Propagation that recovers a provably optimal fraction of community labels.

### Consistency Thresholds for Binary Symmetric Block Models

- Computer Science, MathematicsArXiv
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### Efficient Inference in Stochastic Block Models With Vertex Labels

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### Partial recovery bounds for the sparse stochastic block model

- Computer Science, Mathematics2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

The information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities a/n and b/n respectively, are studied.

### Reconstruction in the labeled stochastic block model

- Computer Science2013 IEEE Information Theory Workshop (ITW)
- 2013

It is shown that when above the threshold by a specific constant, reconstruction is achieved by (1) minimum bisection, and (2) a spectral method combined with removal of nodes of high degree.

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The community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM) is considered, a general model of random networks with community structure and higher-order interactions, and a spectral algorithm is provided that achieves weak consistency.

### Local Algorithms for Block Models with Side Information

- Mathematics, Computer ScienceITCS
- 2016

It is shown that local algorithms achieve optimal performance in the above three regimes for the block model with side information, in contrast to the cases of independent sets or a single community in random graphs and to the case of symmetric block models without side information.

### A sparse stochastic block model with two unequal communities

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### Accuracy-Memory Tradeoffs and Phase Transitions in Belief Propagation

- Computer ScienceCOLT
- 2019

This work proves a conjecture that any recursive algorithm with bounded memory for the reconstruction problem on the trees with the binary symmetric channel has a phase transition strictly below the Belief Propagation threshold, also known as the Kesten-Stigum bound.

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