64 citations · 329 across the 26 of their papers we have counts for
27 papers
Quantized Low-Rank Quantum State Tomography: Hyperbolic Quantization and Riemannian Least-Squares Recovery
HanQin Cai, Longxiu Huang, Juntao You
We study low-rank quantum state tomography from finite-bit Pauli batch responses. To avoid bias introduced by generic quantization, we propose HyperQuant, a mean-preserving hyperbo…
Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling
HanQin Cai, Longxiu Huang, Jing Qin +1
Tensor cross-concentrated sampling (t-CCS) bridges entrywise sampling and t-CUR slice-wise sampling by observing entries only within selected horizontal and lateral slices. Existin…
Robust Spectral Recovery for Dynamical Sampling
HanQin Cai, Longxiu Huang, Tianming Wang +1
We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}…
Property Inheritance for Subtensors in Tensor Train Decompositions
HanQin Cai, Longxiu Huang
Tensor dimensionality reduction is one of the fundamental tools for modern data science. To address the high computational overhead, fiber-wise sampled subtensors that preserve the…
Three-dimensional signal processing: a new approach in dynamical sampling via tensor products
Yisen Wang, Hanqin Cai, Longxiu Huang
The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. Th…
Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery
Paris Giampouras, HanQin Cai, Rene Vidal
In this paper, we focus on a matrix factorization-based approach to recover low-rank {\it asymmetric} matrices from corrupted measurements. We propose an {\it Overparameterized Pre…
Guaranteed Sampling Flexibility for Low-tubal-rank Tensor Completion
Bowen Su, Juntao You, HanQin Cai +1
While Bernoulli sampling is extensively studied in tensor completion, t-CUR sampling approximates low-tubal-rank tensors via lateral and horizontal subtensors. However, both method…
Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent
HanQin Cai, Longxiu Huang, Xiliang Lu +1
This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a nove…
On the Robustness of Cross-Concentrated Sampling for Matrix Completion
HanQin Cai, Longxiu Huang, Chandra Kundu +1
Matrix completion is one of the crucial tools in modern data science research. Recently, a novel sampling model for matrix completion coined cross-concentrated sampling (CCS) has c…
Towards Constituting Mathematical Structures for Learning to Optimize
Jialin Liu, Xiaohan Chen, Zhangyang Wang +2
Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A g…
Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption
HanQin Cai, Zehan Chao, Longxiu Huang +1
We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given te…
Non-convex approaches for low-rank tensor completion under tubal sampling
Zheng Tan, Longxiu Huang, HanQin Cai +1
Tensor completion is an important problem in modern data analysis. In this work, we investigate a specific sampling strategy, referred to as tubal sampling. We propose two novel no…
Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling
HanQin Cai, Longxiu Huang, Pengyu Li +1
While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both samp…
Riemannian CUR Decompositions for Robust Principal Component Analysis
Keaton Hamm, Mohamed Meskini, HanQin Cai
Robust Principal Component Analysis (PCA) has received massive attention in recent years. It aims to recover a low-rank matrix and a sparse matrix from their sum. This paper propos…
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…
Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection
HanQin Cai, Jialin Liu, Wotao Yin
Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we pr…
Curvature-Aware Derivative-Free Optimization
Bumsu Kim, HanQin Cai, Daniel McKenzie +1
The paper discusses derivative-free optimization (DFO), which involves minimizing a function without access to gradients or directional derivatives, only function evaluations. Clas…
Fast Robust Tensor Principal Component Analysis via Fiber CUR Decomposition
HanQin Cai, Zehan Chao, Longxiu Huang +1
We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their…
Estimation of high-dimensional change-points under a group sparsity structure
Hanqing Cai, Tengyao Wang
Change-points are a routine feature of 'big data' observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures an…
Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions
HanQin Cai, Keaton Hamm, Longxiu Huang +1
Low rank tensor approximation is a fundamental tool in modern machine learning and data science. In this paper, we study the characterization, perturbation analysis, and an efficie…
A Zeroth-Order Block Coordinate Descent Algorithm for Huge-Scale Black-Box Optimization
HanQin Cai, Yuchen Lou, Daniel McKenzie +1
We consider the zeroth-order optimization problem in the huge-scale setting, where the dimension of the problem is so large that performing even basic vector operations on the deci…
Robust CUR Decomposition: Theory and Imaging Applications
HanQin Cai, Keaton Hamm, Longxiu Huang +1
This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of m…
Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation
HanQin Cai, Keaton Hamm, Longxiu Huang +2
Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR),…
A One-bit, Comparison-Based Gradient Estimator
HanQin Cai, Daniel Mckenzie, Wotao Yin +1
We study zeroth-order optimization for convex functions where we further assume that function evaluations are unavailable. Instead, one only has access to a $\textit{comparison ora…