• Corpus ID: 240354807

Optimal Reconstruction of General Sparse Stochastic Block Models

@inproceedings{Chin2021OptimalRO,
  title={Optimal Reconstruction of General Sparse Stochastic Block Models},
  author={Byron Chin and Allan Sly},
  year={2021}
}
Abstract. This paper is motivated by the reconstruction problem on the sparse stochastic block model. The paper “Belief Propagation, Robust Reconstruction and Optimal Recovery of Block Models” by Mossel, Neeman, and Sly [6] provided and proved a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The main contribution of their proof is to show that when the signal to noise ratio is sufficiently large, in particular λd > C, the… 

Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model

TLDR
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.

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As the black box algorithm to provide our initial noisy estimates, we will make minor adjustments to the following theorem from Abbe and Sandon

    For any k ∈ Z, p ∈ (0, 1) k with |p| = 1. and symmetric matrix Q with no two rows equal, there exists ǫ(c) such that for all sufficiently large c