3 citations · 3 across the 6 of their papers we have counts for
7 papers · 1 filter
Self-Normalized Inference from Riemannian Stochastic Gradient Paths
Xiaotian Chang, Qirui Hu, Yi Liu
Riemannian stochastic gradient paths estimate constrained parameters, but confidence regions usually require estimating the Hessian and gradient-noise covariance. We develop self-n…
Riemannian Newton Methods with Statistical Inference
Xiaotian Chang, Qirui Hu, Yangdi Jiang +1
We develop online statistical inference for Polyak-Ruppert averages of inexact Newton iterates on Riemannian manifolds. A local asymptotic representation separates observation nois…
Bootstrap Inference for Riemannian Optimization Problems
Xiaotian Chang, Qirui Hu, Yangdi Jiang +1
We develop an online multiplier bootstrap for manifold-valued parameters estimated by averaging the iterates of Riemannian stochastic approximation. The method runs weighted iterat…
Sampling Design and Confidence Tubes for Integral Curves on Riemannian Manifolds
Xiaotian Chang, Qirui Hu, Cyrus Mostajeran
We estimate the integral curve of an unknown vector field from noisy tangent vector field on a known compact Riemannian manifold. We consider two sampling settings: independent obs…
Locally Private Inference for Riemannian Stochastic Optimization
Xiaotian Chang, Yangdi Jiang, Qirui Hu
We develop inference for manifold-valued population minimizers when each observation belongs to a different participant and only locally private messages reach the analyst. The met…
Riemannian Simultaneous Inference for Tangent Vector Field Regression
Xiaotian Chang, Yangdi Jiang, Qirui Hu
We consider nonparametric tangent vector field regression on a Riemannian manifold without boundary. Because responses at different points lie in different tangent spaces, the prop…
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…