47 citations · 84 across the 7 of their papers we have counts for
7 papers
Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning
T. Tony Cai, Yichen Wang, Linjun Zhang
Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the op…
The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds
T. Tony Cai, Yichen Wang, Linjun Zhang
We propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private v…
Estimation, Confidence Intervals, and Large-Scale Hypotheses Testing for High-Dimensional Mixed Linear Regression
Linjun Zhang, Rong Ma, T. Tony Cai +1
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion…
A Convex Optimization Approach to High-Dimensional Sparse Quadratic Discriminant Analysis
T. Tony Cai, Linjun Zhang
In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower…
The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy
T. Tony Cai, Yichen Wang, Linjun Zhang
We study the minimax cost of -differential privacy for mean estimation and Gaussian linear regression in low and high dimensions. For low-dimensional mean estimati…
High-dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm, and Missing Data
T. Tony Cai, Linjun Zhang
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based…