4 papers
Differentially private inference framework for Riemannian manifold data
Yangdi Jiang, Xiaotian Chang, Qirui Hu
We propose a novel and systematic differentially private (DP) inference framework for non-Euclidean data. First, we design two types of DP mechanisms for the Fréchet mean and vari…
Asymptotic Anytime-Valid Inference for U-statistics
Leheng Cai, Qirui Hu, Weijia Li
We study asymptotic anytime-valid confidence sequences for degree-two U-statistics under continuous monitoring. In the nondegenerate case, Hoeffding's projection reduces the proble…
Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms
Xiaotian Chang, Yangdi Jiang, Cyrus Mostajeran +1
In this paper, we develop a novel privacy mechanism for Riemannian manifold-valued data. Our key contribution lies in uncovering unexpected connections among geometric analysis, he…
Strong Gaussian approximation for U-statistics in high dimensions and beyond
Weijia Li, Leheng Cai, Qirui Hu
We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich…