316 citations · 1.7k across the 39 of their papers we have counts for
36 papers · 1 filter
Leave-one-out Singular Subspace Perturbation Analysis for Spectral Clustering
Anderson Y. Zhang, Harrison H. Zhou
The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrar…
Rates of estimation for high-dimensional multi-reference alignment
Zehao Dou, Zhou Fan, Harrison Zhou
We study the continuous multi-reference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-…
Optimal estimation of high-dimensional location Gaussian mixtures
Natalie Doss, Yihong Wu, Pengkun Yang +1
This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of compone…
Optimality of Spectral Clustering in the Gaussian Mixture Model
Matthias Löffler, Anderson Y. Zhang, Harrison H. Zhou
Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successf…
Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in iterations
Yihong Wu, Harrison H. Zhou
We analyze the classical EM algorithm for parameter estimation in the symmetric two-component Gaussian mixtures in dimensions. We show that, even in the absence of any separati…
Theoretical and Computational Guarantees of Mean Field Variational Inference for Community Detection
Anderson Y. Zhang, Harrison H. Zhou
The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative Coordinate Ascent Variational Inference algorithm has bee…
Structured Matrix Estimation and Completion
Olga Klopp, Yu Lu, Alexandre B. Tsybakov +1
We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mi…
Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants
Yu Lu, Harrison H. Zhou
Clustering is a fundamental problem in statistics and machine learning. Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice…
Community Detection in Degree-Corrected Block Models
Chao Gao, Zongming Ma, Anderson Y. Zhang +1
Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of cluster…
Optimal large-scale quantum state tomography with Pauli measurements
Tony Cai, Donggyu Kim, Yazhen Wang +2
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum…
Optimal Estimation and Completion of Matrices with Biclustering Structures
Chao Gao, Yu Lu, Zongming Ma +1
Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such struct…
Minimax Rates of Community Detection in Stochastic Block Models
Anderson Y. Zhang, Harrison H. Zhou
Recently network analysis has gained more and more attentions in statistics, as well as in computer science, probability, and applied mathematics. Community detection for the stoch…
A General Framework for Bayes Structured Linear Models
Chao Gao, Aad W. van der Vaart, Harrison H. Zhou
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies…
Achieving Optimal Misclassification Proportion in Stochastic Block Model
Chao Gao, Zongming Ma, Anderson Y. Zhang +1
Community detection is a fundamental statistical problem in network data analysis. Many algorithms have been proposed to tackle this problem. Most of these algorithms are not guara…
Bernstein-von Mises Theorems for Functionals of Covariance Matrix
Chao Gao, Harrison H. Zhou
We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. R…
Rate-optimal graphon estimation
Chao Gao, Yu Lu, Harrison H. Zhou
Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms…
Minimax estimation in sparse canonical correlation analysis
Chao Gao, Zongming Ma, Zhao Ren +1
Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of est…
Rate exact Bayesian adaptation with modified block priors
Chao Gao, Harrison H. Zhou
A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near…
Rate-optimal posterior contraction for sparse PCA
Chao Gao, Harrison H. Zhou
Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the lead…
Sparse CCA via Precision Adjusted Iterative Thresholding
Mengjie Chen, Chao Gao, Zhao Ren +1
Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. Ho…
Optimal sparse volatility matrix estimation for high-dimensional Itô processes with measurement errors
Minjing Tao, Yazhen Wang, Harrison H. Zhou
Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rat…
Law of Log Determinant of Sample Covariance Matrix and Optimal Estimation of Differential Entropy for High-Dimensional Gaussian Distributions
T. Tony Cai, Tengyuan Liang, Harrison H. Zhou
Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and st…
Asymptotic normality and optimalities in estimation of large Gaussian graphical models
Zhao Ren, Tingni Sun, Cun-Hui Zhang +1
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This pape…
Optimal rates of convergence for sparse covariance matrix estimation
T. Tony Cai, Harrison H. Zhou
This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A…