Spectral methods for data science: A statistical perspective

Y Chen, Y Chi, J Fan, C Ma - Foundations and Trends® in …, 2021 - nowpublishers.com
Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements

T Tong, C Ma, A Prater-Bennette, E Tripp… - Journal of Machine …, 2022 - jmlr.org
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 …

Tensor-on-tensor regression: Riemannian optimization, over-parameterization, statistical-computational gap and their interplay

Y Luo, AR Zhang - The Annals of Statistics, 2024 - projecteuclid.org
Tensor-on-tensor regression: Riemannian optimization, over-parameterization, statistical-computational
gap and their interplay Page 1 The Annals of Statistics 2024, Vol. 52, No. 6, 2583–2612 …

Fast and provable tensor robust principal component analysis via scaled gradient descent

H Dong, T Tong, C Ma, Y Chi - … and Inference: A Journal of the …, 2023 - academic.oup.com
An increasing number of data science and machine learning problems rely on computation
with tensors, which better capture the multi-way relationships and interactions of data than …

Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization

C Ma, X Xu, T Tong, Y Chi - arXiv preprint arXiv:2310.06159, 2023 - arxiv.org
Many problems encountered in science and engineering can be formulated as estimating a
low-rank object (eg, matrices and tensors) from incomplete, and possibly corrupted, linear …

Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gaps

W Ma, D Xia - arXiv preprint arXiv:2410.11225, 2024 - arxiv.org
This paper presents a simple yet efficient method for statistical inference of tensor linear
forms using incomplete and noisy observations. Under the Tucker low-rank tensor model …

Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent

Z Liu, Z Han, Y Tang, XL Zhao, Y Wang - arXiv preprint arXiv:2401.11940, 2024 - arxiv.org
This paper considers the problem of recovering a tensor with an underlying low-tubal-rank
structure from a small number of corrupted linear measurements. Traditional approaches …

Leave-One-Out Analysis for Nonconvex Robust Matrix Completion with General Thresholding Functions

T Wang, K Wei - arXiv preprint arXiv:2407.19446, 2024 - arxiv.org
We study the problem of robust matrix completion (RMC), where the partially observed
entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the …

A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Rank Tensor Recovery

Y Zhang, YN Zhu, X Zhang - arXiv preprint arXiv:2401.15925, 2024 - arxiv.org
This paper focuses on recovering a low-rank tensor from its incomplete measurements. We
propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent …

Provably Accelerating Ill-Conditioned Low-Rank Estimation via Scaled Gradient Descent, Even with Overparameterization

C Ma, X Xu, T Tong, Y Chi - Explorations in the Mathematics of Data …, 2024 - Springer
Many problems encountered in data science can be formulated as estimating a low-rank
object (eg, matrices and tensors) from incomplete, and possibly corrupted, linear …