Distribution of Distances based Object Matching: Asymptotic Inference

• 成果类型: Article
• 署名作者: Weitkamp, Christoph Alexander; Proksch, Katharina; Tameling, Carla; Munk, Axel
• 署名单位: University of Gottingen; University of Twente; Max Planck Society
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2127360
• 发表日期: 2024
• 页码: 538-551
• 关键词: protein-structure alignment; empirical quantile process; helicase prp43; u-processes; statistics; Similarity; RECOGNITION; activation; tests

摘要

In this article, we aim to provide a statistical theory for object matching based on a lower bound of the Gromov-Wasserstein distance related to the distribution of (pairwise) distances of the considered objects. To this end, we model general objects as metric measure spaces. Based on this, we propose a simple and efficiently computable asymptotic statistical test for pose invariant object discrimination. This is based on a (beta-trimmed) empirical version of the afore-mentioned lower bound. We derive the distributional limits of this test statistic for the trimmed and untrimmed case. For this purpose, we introduce a novel U-type process indexed in t and show its weak convergence. The theory developed is investigated in Monte Carlo simulations and applied to structural protein comparisons. Supplementary materials for this article are available online.