15 citations · 29 across the 13 of their papers we have counts for
13 papers
Online Riemannian Gradient Descent for Quantum State Tomography with Matrix Product Operators
Jian-Feng Cai, Jingyang Li, Xiaoqun Zhang +1
Matrix product operators (MPOs) provide a scalable approach for quantum state tomography (QST) by offering a compact representation of many-body mixed states with limited entanglem…
Uncertainty Quantification for Noisy Low-tubal-rank Tensor Completion
Jiuqian Shang, Jingyang Li, Yang Chen
High-dimensional tensor data often exhibit strong temporal correlations that appear as low-dimensional structures in the frequency domain. While the low-tubal-rank tensor model eff…
Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm
Jingyang Li, T. Tony Cai, Dong Xia +1
Federated Learning (FL) has gained significant recent attention in machine learning for its enhanced privacy and data security, making it indispensable in fields such as healthcare…
Online Policy Learning and Inference by Matrix Completion
Congyuan Duan, Jingyang Li, Dong Xia
Is it possible to make online decisions when personalized covariates are unavailable? We take a collaborative-filtering approach for decision-making based on collective preferences…
Restoration Guarantee of Image Inpainting via Low Rank Patch Matrix Completion
Jian-Feng Cai, Jae Kyu Choi, Jingyang Li +1
In recent years, patch-based image restoration approaches have demonstrated superior performance compared to conventional variational methods. This paper delves into the mathematic…
Nonconvex Stochastic Bregman Proximal Gradient Method with Application to Deep Learning
Kuangyu Ding, Jingyang Li, Kim-Chuan Toh
Stochastic gradient methods for minimizing nonconvex composite objective functions typically rely on the Lipschitz smoothness of the differentiable part, but this assumption fails…
Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret
Jingyang Li, Jian-Feng Cai, Yang Chen +1
Large tensor learning algorithms are typically computationally expensive and require storing a vast amount of data. In this paper, we propose a unified online Riemannian gradient d…
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…
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…
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…
Provable Tensor-Train Format Tensor Completion by Riemannian Optimization
Jian-Feng Cai, Jingyang Li, Dong Xia
The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from…
Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization
Jian-Feng Cai, Jingyang Li, Dong Xia
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…
Image Restoration: Structured Low Rank Matrix Framework for Piecewise Smooth Functions and Beyond
Jian-Feng Cai, Jae Kyu Choi, Jingyang Li +1
Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate…