Spectral methods for data science: A statistical perspective
Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements
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 …
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
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 …
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
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 …
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
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 …
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
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 …
forms using incomplete and noisy observations. Under the Tucker low-rank tensor model …
Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent
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 …
structure from a small number of corrupted linear measurements. Traditional approaches …
Leave-One-Out Analysis for Nonconvex Robust Matrix Completion with General Thresholding Functions
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 …
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 …
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
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 …
object (eg, matrices and tensors) from incomplete, and possibly corrupted, linear …