Empirical optimal transport under estimated costs: Distributional limits and statistical applications

Shayan Hundrieser, Gilles Mordant, Christoph A. Weitkamp and Axel Munk

Stochastic Processes and their Applications, 2024, vol. 178, issue C

Abstract: Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This is addressed in this paper with the derivation of distributional limits for the empirical OT value when the cost function and the measures are estimated from data. For statistical inference purposes, but also from the viewpoint of a stability analysis, understanding the fluctuation of such quantities is paramount. Our results find direct application in the problem of goodness-of-fit testing for group families, in machine learning applications where invariant transport costs arise, in the problem of estimating the distance between mixtures of distributions, and for the analysis of empirical sliced OT quantities.

Keywords: Optimal transport; Central limit theorem; Stability analysis; Curse of dimensionality; Empirical process; Bootstrap (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414924001686
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:178:y:2024:i:c:s0304414924001686

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2024.104462

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().