Interpretable Stein Goodness-of-fit Tests on Riemannian Manifolds

2021/03/01 by Wenkai Xu, Xu, Wenkai, Takeru Matsuda +1 · 2 citations
Mathematics · #FOS: Computer and information sciences #Geometric Analysis and Curvature Flows #Methodology (stat.ME) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2103.00895

openalex publication_date 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In many applications, we encounter data on Riemannian manifolds such as torus and rotation groups. Standard statistical procedures for multivariate data are not applicable to such data. In this study, we develop goodness-of-fit testing and interpretable model criticism methods for general distributions on Riemannian manifolds, including those with an intractable normalization constant. The proposed methods are based on extensions of kernel Stein discrepancy, which are derived from Stein operators on Riemannian manifolds. We discuss the connections between the proposed tests with existing ones and provide a theoretical analysis of their asymptotic Bahadur efficiency. Simulation results and real data applications show the validity of the proposed methods.

Citations

• Probabilistic model for two dependent circular variables
• A Wild Bootstrap for Degenerate Kernel Tests
• Large sample analysis of the median heuristic
• A diffusion approach to Stein's method on Riemannian manifolds
• Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data

Cited by

• Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD
• The Minimax Lower Bound of Kernel Stein Discrepancy Estimation

Related

• Theory and Applications of Kernel Stein's Method on Riemannian Manifolds
• A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation
• A Framework for Improving the Characterization Scope of Stein's Method on Riemannian Manifolds
• A Stein Goodness-of-fit Test for Directional Distributions
• Goodness-of-fit tests on manifolds