Principal component analysis (PCA) is a widely used technique for dimension reduction,
data processing, and feature extraction. The three tasks are particularly useful and important …

Statistical Foundations of Data Science gives a thorough introduction to commonly used
statistical models, contemporary statistical machine learning techniques and algorithms …

Optimization problems with rank constraints arise in many applications, including matrix
regression, structured PCA, matrix completion and matrix decomposition problems. An …

We describe a general technique that yields the first Statistical Query lower bounds for a
range of fundamental high-dimensional learning problems involving Gaussian distributions …

We study the problem of estimating the trace of a matrix A that can only be accessed through
matrix-vector multiplication. We introduce a new randomized algorithm, Hutch++, which …

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

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a
generalized and unified asymptotic regime, which takes into account the magnitude of …

Sparse PCA: Optimal rates and adaptive estimation Page 1 The Annals of Statistics 2013, Vol.
41, No. 6, 3074–3110 DOI: 10.1214/13-AOS1178 © Institute of Mathematical Statistics, 2013 …

This is an expository paper that reviews recent developments on optimal estimation of
structured high-dimensional covariance and precision matrices. Minimax rates of …

When the data are high dimensional, widely used multivariate statistical methods such as
principal component analysis can behave in unexpected ways. In settings where the …