Substantial progress has been made recently on developing provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

This article provides an overview of tensors, their properties, and their applications in
statistics. Tensors, also known as multidimensional arrays, are generalizations of matrices to …

This paper considers the problem of solving systems of quadratic equations, namely,
recovering an object of interest x^ ♮ ∈ R^ nx♮∈ R n from m quadratic equations/samples …

We study a completion problem of broad practical interest: the reconstruction of a low-rank
symmetric tensor from highly incomplete and randomly corrupted observations of its entries …

An optimal statistical and computational framework for generalized tensor estimation Page 1 The
Annals of Statistics 2022, Vol. 50, No. 1, 1–29 https://doi.org/10.1214/21-AOS2061 © Institute of …

Heteroskedastic PCA: Algorithm, optimality, and applications Page 1 The Annals of Statistics
2022, Vol. 50, No. 1, 53–80 https://doi.org/10.1214/21-AOS2074 © Institute of Mathematical …

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 …

Tensors, which provide a powerful and flexible model for representing multi-attribute data
and multi-way interactions, play an indispensable role in modern data science across …

In this article, we consider the sparse tensor singular value decomposition, which aims for
dimension reduction on high-dimensional high-order data with certain sparsity structure. A …

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor,
where the low-rank tensor often captures the multi-way principal components and the sparse …