3 papers
stat.ME2026
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…
math.ST2026
Horospherical Depth and Busemann Median on Hadamard Manifolds
Yangdi Jiang, Xiaotian Chang, Cyrus Mostajeran
\We introduce the horospherical depth, an intrinsic notion of statistical depth on Hadamard manifolds, and define the Busemann median as the set of its maximizers. The construction…
stat.ML2026
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…