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

In this paper, we propose a general framework for tensor singular value decomposition
(tensor singular value decomposition (SVD)), which focuses on the methodology and theory …

This paper investigates the theoretical foundations of the t-distributed stochastic neighbor
embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data …

This paper is concerned with the problem of reconstructing an unknown rank-one matrix with
prior structural information from noisy observations. While computing the Bayes optimal …

In statistics and machine learning, we are interested in the eigenvectors (or singular vectors)
of certain matrices (eg covariance matrices, data matrices, etc). However, those matrices are …

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

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 …

We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian
from a single pair of generic initial and final states related by evolving with the Hamiltonian …

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 …

Multimodal single-cell technologies profile multiple modalities for each cell simultaneously,
enabling a more thorough characterization of cell populations. Existing dimension-reduction …