High-dimensional probability offers insight into the behavior of random vectors, random
matrices, random subspaces, and objects used to quantify uncertainty in high dimensions …

Recovering low-rank structures via eigenvector perturbation analysis is a common problem
in statistical machine learning, such as in factor analysis, community detection, ranking …

This paper surveys recent theoretical advances in convex optimization approaches for
community detection. We introduce some important theoretical techniques and results for …

Semidefinite programs (SDP's) can be solved in polynomial time by interior point methods,
but scalability can be an issue. To address this shortcoming, over a decade ago, Burer and …

This paper is concerned with the problem of reconstructing an unknown rank-one matrix with
prior structural information from noisy observations. While computing the Bayes optimal …

We estimate n phases (angles) from noisy pairwise relative phase measurements. The task
is modeled as a nonconvex least-squares optimization problem. It was recently shown that …

Precise statistical analysis of classification accuracies for adversarial training Page 1 The
Annals of Statistics 2022, Vol. 50, No. 4, 2127–2156 https://doi.org/10.1214/22-AOS2180 © …

The problem of estimating the phases (angles) of a complex unit-modulus vector z from their
noisy pairwise relative measurements C=zz^*+σW, where W is a complex-valued Gaussian …

A central problem of random matrix theory is to understand the eigenvalues of spiked
random matrix models, introduced by Johnstone, in which a prominent eigenvector (or …

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 …