Self-Normalized Inference from Riemannian Stochastic Gradient Paths
Abstract
Riemannian stochastic gradient paths estimate constrained parameters, but confidence regions usually require estimating the Hessian and gradient-noise covariance. We develop self-normalized inference from one path by expressing retained iterates in a common random tangent space. Their average and centered partial sums share an unknown covariance factor that cancels in a Brownian bridge pivot. Under suitable regularity conditions, a joint expansion of the averaged estimator and integrated path controls nonlinear coordinate errors using conditional second moments. The procedure uses fixed-dimensional memory and extends to nondegenerate smooth functionals and alternative local coordinates. Numerical studies show competitive coverage relative to plug-in Wald inference while avoiding Hessian and residual-density estimation.
Related
- Online Covariance Estimation for Averaged Stochastic Gradient Descent on Riemannian Manifolds
- Locally Private Inference for Riemannian Stochastic Optimization
- Lower Bounds on Inference Complexity for Polyak-Ruppert Averaged Stochastic Gradient Descent
- Scalable Statistical Inference in Stochastic Gradient Descent
- Finite volume discretization and normalized gradient flow for computing minimizers of the rotating Gross-Pitaevskii energy
BibTeX
@misc{chang2026selfnormalized,
title = {{Self-Normalized Inference from Riemannian Stochastic Gradient Paths}},
author = {Xiaotian Chang and Qirui Hu and Yi Liu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01035},
eprint = {2611.01035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01035},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Self-Normalized Inference from Riemannian Stochastic Gradient Paths
AU - Xiaotian Chang
AU - Qirui Hu
AU - Yi Liu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01035
UR - https://arxiv.org/abs/2611.01035
AB - Riemannian stochastic gradient paths estimate constrained parameters, but confidence regions usually require estimating the Hessian and gradient-noise covariance. We develop self-normalized inference from one path by expressing retained iterates in a common random tangent space. Their average and centered partial sums share an unknown covariance factor that cancels in a Brownian bridge pivot. Under suitable regularity conditions, a joint expansion of the averaged estimator and integrated path controls nonlinear coordinate errors using conditional second moments. The procedure uses fixed-dimensional memory and extends to nondegenerate smooth functionals and alternative local coordinates. Numerical studies show competitive coverage relative to plug-in Wald inference while avoiding Hessian and residual-density estimation.
ER -