80 citations · 602 across the 56 of their papers we have counts for
6 papers · 1 filter
Concentration of random graphs and application to community detection
Can M. Le, Elizaveta Levina, Roman Vershynin
Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random grap…
Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization
Jess Banks, Cristopher Moore, Nicolas Verzelen +2
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and…
Sparse random graphs: regularization and concentration of the Laplacian
Can M. Le, Elizaveta Levina, Roman Vershynin
We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacenc…
Community detection in sparse networks via Grothendieck's inequality
Olivier Guédon, Roman Vershynin
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 pr…
Estimation in high dimensions: a geometric perspective
Roman Vershynin
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about hi…
Partial estimation of covariance matrices
Elizaveta Levina, Roman Vershynin
A classical approach to accurately estimating the covariance matrix Σof a p-variate normal distribution is to draw a sample of size n > p and form a sample covariance matrix. Howev…