The stochastic block model (SBM) is a random graph model with planted clusters. It is widely
employed as a canonical model to study clustering and community detection, and provides …

The principal submatrix localization problem deals with recovering a K× K principal
submatrix of elevated mean µ in a large n× n symmetric matrix subject to additive standard …

New phase transition phenomena have recently been discovered for the stochastic block
model, for the special case of two non-overlapping symmetric communities. This gives raise …

Community detection is a fundamental statistical problem in network data analysis. In this
paper, we present a polynomial time two-stage method that provably achieves optimal …

In this paper, we propose a general framework for tensor singular value decomposition
(tensor singular value decomposition (SVD)), which focuses on the methodology and theory …

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 independently …

Supplement to “Mimimax rates of community detection in stochastic block models”. In the
supplement 31, we provide proofs of Lemma 5.2, Propositions 5.1 and 5.2. We also provide …

We present a simple and flexible method to prove consistency of semidefinite optimization
problems on random graphs. The method is based on Grothendieck's inequality. Unlike the …

On semidefinite relaxations for the block model Page 1 The Annals of Statistics 2018, Vol. 46,
No. 1, 149–179 https://doi.org/10.1214/17-AOS1545 © Institute of Mathematical Statistics …

Denote by A the adjacency matrix of an Erdos-Renyi graph with bounded average degree.
We consider the problem of maximizing< A-EA, X> over the set of positive semidefinite …