82 citations · 384 across the 49 of their papers we have counts for
50 papers
Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model
Runshi Tang, Ming Yuan, Anru R. Zhang
This paper introduces a novel framework called Mode-wise Principal Subspace Pursuit (MOP-UP) to extract hidden variations in both the row and column dimensions for matrix data. To…
Phase transition for detecting a small community in a large network
Jiashun Jin, Zheng Tracy Ke, Paxton Turner +1
How to detect a small community in a large network is an interesting problem, including clique detection as a special case, where a naive degree-based -test was shown to be po…
Enhancing convolutional neural network generalizability via low-rank weight approximation
Chenyin Gao, Shu Yang, Anru R. Zhang
Noise is ubiquitous during image acquisition. Sufficient denoising is often an important first step for image processing. In recent decades, deep neural networks (DNNs) have been w…
Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
Sitan Chen, Sinho Chewi, Jerry Li +3
We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of la…
Core Shrinkage Covariance Estimation for Matrix-variate Data
Peter Hoff, Andrew McCormack, Anru R. Zhang
A separable covariance model for a random matrix provides a parsimonious description of the covariances among the rows and among the columns of the matrix, and permits likelihood-b…
One-dimensional Tensor Network Recovery
Ziang Chen, Jianfeng Lu, Anru R. Zhang
We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after…
Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay
Yuetian Luo, Anru R. Zhang
We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowle…
Discussion of "Vintage factor analysis with Varimax performs statistical inference"
Rungang Han, Anru R. Zhang
We wholeheartedly congratulate Drs. Rohe and Zeng for their insightful paper \cite{rohe2020vintage} on vintage factor analysis with Varimax rotation. This note discusses the condit…
Learning Polynomial Transformations
Sitan Chen, Jerry Li, Yuanzhi Li +1
We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form , where is hidden and $p:…
On Geometric Connections of Embedded and Quotient Geometries in Riemannian Fixed-rank Matrix Optimization
Yuetian Luo, Xudong Li, Anru R. Zhang
In this paper, we propose a general procedure for establishing the geometric landscape connections of a Riemannian optimization problem under the embedded and quotient geometries.…
Guaranteed Functional Tensor Singular Value Decomposition
Rungang Han, Pixu Shi, Anru R. Zhang
This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular mod…
Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimization
Yuetian Luo, Xudong Li, Anru R. Zhang
In this paper, we consider the geometric landscape connection of the widely studied manifold and factorization formulations in low-rank positive semidefinite (PSD) and general matr…
Learning Good State and Action Representations via Tensor Decomposition
Chengzhuo Ni, Yaqi Duan, Munther Dahleh +2
The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning meth…
Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence
Yuetian Luo, Anru R. Zhang
In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from app…
Inference for Low-rank Tensors -- No Need to Debias
Dong Xia, Anru R. Zhang, Yuchen Zhou
In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any esti…
Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit
Rungang Han, Yuetian Luo, Miaoyan Wang +1
High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex a…
Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
Yuetian Luo, Wen Huang, Xudong Li +1
In this paper, we propose {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \…
Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration
Yuchen Zhou, Anru R. Zhang, Lili Zheng +1
This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estim…
Open Problem: Average-Case Hardness of Hypergraphic Planted Clique Detection
Yuetian Luo, Anru R. Zhang
We note the significance of hypergraphic planted clique (HPC) detection in the investigation of computational hardness for a range of tensor problems. We ask if more evidence for t…
On the Non-Asymptotic Concentration of Heteroskedastic Wishart-type Matrix
T. Tony Cai, Rungang Han, Anru R. Zhang
This paper focuses on the non-asymptotic concentration of the heteroskedastic Wishart-type matrices. Suppose is a -by- random matrix and i…
A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration
Yuetian Luo, Garvesh Raskutti, Ming Yuan +1
In this paper, we develop novel perturbation bounds for the high-order orthogonal iteration (HOOI) [DLDMV00b]. Under mild regularity conditions, we establish blockwise tensor pertu…
A Schatten- Low-rank Matrix Perturbation Analysis via Perturbation Projection Error Bound
Yuetian Luo, Rungang Han, Anru R. Zhang
This paper studies the Schatten- error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on the lo…
Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits
Yuetian Luo, Anru R. Zhang
This paper studies the statistical and computational limits of high-order clustering with planted structures. We focus on two clustering models, constant high-order clustering (CHC…
An Optimal Statistical and Computational Framework for Generalized Tensor Estimation
Rungang Han, Rebecca Willett, Anru R. Zhang
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imag…