It is known that the common factors in a large panel of data can be consistently estimated by
the method of principal components, and principal components can be constructed by …

In the 1930s, Psychologists began developing Multiple-Factor Analysis to decompose
multivariate data into a small number of interpretable factors without any a priori knowledge …

It is known that the common factors in a large panel of data can be consistently estimated by
the method of principal components, and principal components can be constructed by …

This paper addresses the sparse principal component analysis (SPCA) problem for
covariance matrices in dimension n aiming to find solutions with sparsity k using mixed …

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of
fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that …

We propose a framework for modeling and solving low-rank optimization problems to
certifiable optimality. We introduce symmetric projection matrices that satisfy Y 2= Y, the …

We describe a randomized algorithm for producing a near-optimal hierarchical off-diagonal
low-rank (HODLR) approximation to an n× n matrix A, accessible only though matrix-vector …

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of
decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank …

A key question in many low-rank problems throughout optimization, machine learning, and
statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply …

Inferring the covariance matrix of multivariate data is of great interest in statistics, finance,
and data science. It is often carried out via the maximum likelihood estimation (MLE) …