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The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds

Nov 08, 2020
T. Tony Cai, Yichen Wang, Linjun Zhang

* 43 pages, 6 figures 

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Estimation, Confidence Intervals, and Large-Scale Hypotheses Testing for High-Dimensional Mixed Linear Regression

Nov 06, 2020
Linjun Zhang, Rong Ma, T. Tony Cai, Hongzhe Li


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Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control

Oct 21, 2020
Sai Li, T. Tony Cai, Hongzhe Li


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Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality

Jun 18, 2020
Sai Li, T. Tony Cai, Hongzhe Li


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Optimal Structured Principal Subspace Estimation: Metric Entropy and Minimax Rates

Feb 23, 2020
T. Tony Cai, Hongzhe Li, Rong Ma


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Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms

Jan 24, 2020
T. Tony Cai, Hongji Wei


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High Dimensional M-Estimation with Missing Outcomes: A Semi-Parametric Framework

Nov 26, 2019
Abhishek Chakrabortty, Jiarui Lu, T. Tony Cai, Hongzhe Li

* 34 pages, 4 tables; (Supplement: 58 pages, 10 tables); 

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Sparse Group Lasso: Optimal Sample Complexity, Convergence Rate, and Statistical Inference

Sep 21, 2019
T. Tony Cai, Anru Zhang, Yuchen Zhou


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Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier

Jun 07, 2019
T. Tony Cai, Hongji Wei


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The Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential Privacy

Feb 12, 2019
T. Tony Cai, Yichen Wang, Linjun Zhang

* 34 pages, 6 figures 

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Heteroskedastic PCA: Algorithm, Optimality, and Applications

Oct 19, 2018
Anru Zhang, T. Tony Cai, Yihong Wu


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Semi-supervised Inference: General Theory and Estimation of Means

Aug 14, 2018
Anru Zhang, Lawrence D. Brown, T. Tony Cai


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Weighted Message Passing and Minimum Energy Flow for Heterogeneous Stochastic Block Models with Side Information

Sep 12, 2017
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin

* 31 pages, 1 figures 

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Matrix Completion via Max-Norm Constrained Optimization

Apr 28, 2017
T. Tony Cai, Wen-Xin Zhou

* 33 pages 

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On Detection and Structural Reconstruction of Small-World Random Networks

Apr 21, 2016
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin

* 22 pages, 3 figures 

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Inference via Message Passing on Partially Labeled Stochastic Block Models

Mar 22, 2016
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin

* 33 pages, 4 figures 

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A Sparse PCA Approach to Clustering

Feb 16, 2016
T. Tony Cai, Linjun Zhang

* This paper is part of a discussion of the paper "Important feature PCA for high dimensional clustering" by Jiashun Jin and Wanjie Wang to appear in The Annals of Statistics 

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Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix

Oct 21, 2015
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin

* 37 pages, 1 figure 

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Geometric Inference for General High-Dimensional Linear Inverse Problems

Jun 16, 2015
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin

* 39 pages, 6 figures 

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Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow

Jun 10, 2015
T. Tony Cai, Xiaodong Li, Zongming Ma

* 28 pages, 4 figures 

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Robust and computationally feasible community detection in the presence of arbitrary outlier nodes

Jun 03, 2015
T. Tony Cai, Xiaodong Li

* Annals of Statistics 2015, Vol. 43, No. 3, 1027-1059 
* Published at http://dx.doi.org/10.1214/14-AOS1290 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Structured Matrix Completion with Applications to Genomic Data Integration

Apr 08, 2015
Tianxi Cai, T. Tony Cai, Anru Zhang

* Accepted for publication in Journal of the American Statistical Association 

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ROP: Matrix recovery via rank-one projections

Dec 09, 2014
T. Tony Cai, Anru Zhang

* Annals of Statistics 2015, Vol. 43, No. 1, 102-138 
* Published in at http://dx.doi.org/10.1214/14-AOS1267 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Rate-Optimal Detection of Very Short Signal Segments

Jul 10, 2014
T. Tony Cai, Ming Yuan


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Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices

Oct 22, 2013
T. Tony Cai, Anru Zhang

* to appear in IEEE Transactions on Information Theory 

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A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion

Sep 24, 2013
T. Tony Cai, Wen-Xin Zhou

* 33 pages, 3 figures 

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On Recovery of Sparse Signals via $\ell_1$ Minimization

May 01, 2008
T. Tony Cai, Guangwu Xu, Jun Zhang


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