82 citations · 384 across the 49 of their papers we have counts for
7 papers · 1 filter
High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis
Pixu Shi, Yuchen Zhou, Anru R. Zhang
In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes…
On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables
Anru R. Zhang, Yuchen Zhou
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail prob…
Heteroskedastic PCA: Algorithm, Optimality, and Applications
Anru R. Zhang, T. Tony Cai, Yihong Wu
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iterativ…
Optimal Sparse Singular Value Decomposition for High-dimensional High-order Data
Anru Zhang, Rungang Han
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure.…
Estimation of Markov Chain via Rank-Constrained Likelihood
Xudong Li, Mengdi Wang, Anru Zhang
This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statis…
Spectral State Compression of Markov Processes
Anru Zhang, Mengdi Wang
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the stat…
Sparse and Low-rank Tensor Estimation via Cubic Sketchings
Botao Hao, Anru Zhang, Guang Cheng
In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse te…