585 citations · 1.7k across the 57 of their papers we have counts for
8 papers · 1 filter
Semi-supervised Inference: General Theory and Estimation of Means
Anru Zhang, Lawrence D. Brown, T. Tony Cai
We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of…
Optimal Estimation of Co-heritability in High-dimensional Linear Models
Zijian Guo, Wanjie Wang, T. Tony Cai +1
Co-heritability is an important concept that characterizes the genetic associations within pairs of quantitative traits. There has been significant recent interest in estimating th…
Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data
T. Tony Cai, Anru Zhang
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations…
Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics
T. Tony Cai, Anru Zhang
Perturbation bounds for singular spaces, in particular Wedin's theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning, and…
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…
Inference via Message Passing on Partially Labeled Stochastic Block Models
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin
We study the community detection and recovery problem in partially-labeled stochastic block models (SBM). We develop a fast linearized message-passing algorithm to reconstruct labe…