Distribution of Distances based Object Matching: Asymptotic Inference

Weitkamp, Christoph Alexander; Proksch, Katharina; Tameling, Carla; Munk, Axel

doi:10.1080/01621459.2022.2127360

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Distribution of Distances based Object Matching: Asymptotic Inference

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Munk, Axel
Research Group of Statistical Inverse Problems in Biophysics, Max Planck Institute for Multidisciplinary Sciences, Max Planck Society;

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Citation

Weitkamp, C. A., Proksch, K., Tameling, C., & Munk, A. (2022). Distribution of Distances based Object Matching: Asymptotic Inference. Journal of the American Statistical Association, in press. doi:10.1080/01621459.2022.2127360.

Cite as: https://hdl.handle.net/21.11116/0000-000C-942A-E

Abstract

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 (β-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 β 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.