Year: 2014
Type: preprint
Abstract: The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across clusters. In the asymptotic regime of $p=a \log n/n$ and $q=b \log n/n$ for fixed $a,b$ and $n \to \infty$, we show that the semidefinite programming relaxation of the maximum likelihood estimator achieves the optimal threshold for exactly recovering the partition from the graph with probability tending to one, resolving a conjecture of Abbe et al. \cite{Abbe14}. Furthermore, we show that the semidefinite programming relaxation also achieves the optimal recovery threshold in the planted dense subgraph model containing a single cluster of size proportional to $n$.
Source: arXiv (Cornell University)
Authors: Hajek, Bruce, Wu, Yihong, Xu, Jiaming
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G116299712, G241557827, CIF: Medium: Collaborative Research: Content Delivery over Heterogeneous Networks: Fundamental Limits and Distributed Algorithms, G4094641253, Network Landscape of Photothermal Flowering in Soybean, G4746377364, BIGDATA: F: DKA: CSD: DKM: Theory and Algorithms for Processing Data with Sparse and Multilinear Structure, CIF: Small: Collaborative Research: Sketching and Tracking of Covariance Structures for High-dimensional Streaming Data, INFERENCE AND DYNAMICS ON NETWORKS, G8876996369
OpenAlex ID: W1825700702