134 citations · 644 across the 51 of their papers we have counts for
52 papers
Near-Optimal Nonconvex Matrix Completion
Jian-Feng Cai, Xiliang Lu, Juntao You
We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries. Convex methods achieve sample complexity linear in the m…
Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression
Yinan Shen, Jingyang Li, Jian-Feng Cai +1
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statist…
A Preconditioned Riemannian Gradient Descent Algorithm for Low-Rank Matrix Recovery
Fengmiao Bian, Jian-Feng Cai, Rui Zhang
The low-rank matrix recovery problem often arises in various fields, including signal processing, machine learning, and imaging science. The Riemannian gradient descent (RGD) algor…
Provable Sample-Efficient Sparse Phase Retrieval Initialized by Truncated Power Method
Jian-Feng Cai, Jingyang Li, Juntao You
We study the sparse phase retrieval problem, recovering an -sparse length- signal from magnitude-only measurements. Two-stage non-convex approaches have drawn much attent…
Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion
HanQin Cai, Jian-Feng Cai, Juntao You
We study the robust matrix completion problem for the low-rank Hankel matrix, which detects the sparse corruptions caused by extreme outliers while we try to recover the original H…
Computationally Efficient and Statistically Optimal Robust Low-rank Matrix and Tensor Estimation
Yinan Shen, Jingyang Li, Jian-Feng Cai +1
Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from…