3 papers
math.ST2026
The Cost of Discretization in Functional Linear Regression: Minimax Rates and Adaptation
T. Tony Cai, Yicheng Li
We study scalar-on-function linear regression when each covariate curve is observed only through finitely many noisy point evaluations. Our goal is to characterize the minimax esti…
cs.LG2026
A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning
T. Tony Cai, Yicheng Li
Federated differentially private protocols can communicate over many adaptive rounds and reuse each client's local samples. Existing lower bound arguments for federated DP are ofte…
math.ST2026
Minimax and Adaptive Covariance Matrix Estimation under Differential Privacy
T. Tony Cai, Yicheng Li
Estimating covariance matrices is fundamental to a wide range of statistical applications. This paper studies minimax and adaptive estimation of high-dimensional covariance matrice…