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

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

Supplement to “Rate-optimal perturbation bounds for singular subspaces with applications
to high-dimensional statistics”. The supplementary material includes the proofs for Theorem …

This article provides a selective overview of the recent developments in factor models and
their applications in econometric learning. We focus on the perspective of the low-rank …

This paper is concerned with the problem of top-K ranking from pairwise comparisons. Given
a collection of n items and a few pairwise comparisons across them, one wishes to identify …

The singular value matrix decomposition plays a ubiquitous role throughout statistics and
related fields. Myriad applications including clustering, classification, and dimensionality …

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 …

An lp theory of PCA and spectral clustering Page 1 The Annals of Statistics 2022, Vol. 50, No.
4, 2359–2385 https://doi.org/10.1214/22-AOS2196 © Institute of Mathematical Statistics, 2022 …

Matrix completion is the study of recovering an underlying matrix from a sparse subset of
noisy observations. Traditionally, it is assumed that the entries of the matrix are “missing …

Subspace estimation from unbalanced and incomplete data matrices: l2,infty statistical
guarantees Page 1 The Annals of Statistics 2021, Vol. 49, No. 2, 944–967 https://doi.org/10.1214/20-AOS1986 …