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 random dot product graph (RDPG) is an independent-edge random graph that is
analytically tractable and, simultaneously, either encompasses or can successfully …

Given the unprecedented availability of data and computing resources, there is widespread
renewed interest in applying data-driven machine learning methods to problems for which …

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 …

Modern neural networks are typically trained in an over-parameterized regime where the
parameters of the model far exceed the size of the training data. Such neural networks in …

Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

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

Random matrices now play a role in many areas of theoretical, applied, and computational
mathematics. Therefore, it is desirable to have tools for studying random matrices that are …

Traditionally, community detection in graphs can be solved using spectral methods or
posterior inference under probabilistic graphical models. Focusing on random graph …

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