Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BIGOT, Jérémie | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CAZELLES, Elsa | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAPADAKIS, Nicolas | |
| dc.date.accessioned | 2024-04-04T03:06:03Z | |
| dc.date.available | 2024-04-04T03:06:03Z | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 2049-8764 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193306 | |
| dc.description.abstractEn | We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a d-dimensional Euclidean space. This work is motivated by applications in bio-informatics where researchers aim to automatically normalize large datasets to compare and analyze characteristics within a same cell population. Inconveniently, the information acquired is noisy due to mis-alignment caused by technical variations of the environment. To overcome this problem, we propose to register multiple point clouds by using the notion of regularized barycenter (or Fr\'echet mean) of a set of probability measures with respect to the Wasserstein metric which allows to smooth such data and to remove mis-alignment effect in the sample acquisition process. A first approach consists in penalizing a Wasserstein barycenter with a convex functional as recently proposed in Bigot and al. (2018). A second strategy is to modify the Wasserstein metric itself by using an entropically regularized transportation cost between probability measures as introduced in Cuturi (2013). The main contribution of this work is to propound data-driven choices for the regularization parameters involved in each approach using the Goldenshluger-Lepski's principle. Simulated data sampled from Gaussian mixtures are used to illustrate each method, and an application to the analysis of flow cytometry data is finally proposed. | |
| dc.description.sponsorship | Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010 | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.title.en | Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1093/imaiai/iaz023 | |
| dc.subject.hal | Statistiques [stat]/Machine Learning [stat.ML] | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| dc.subject.hal | Statistiques [stat]/Applications [stat.AP] | |
| dc.identifier.arxiv | 1804.08962 | |
| bordeaux.journal | Information and Inference | |
| bordeaux.page | 719-755 | |
| bordeaux.volume | 8 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01790015 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01790015v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Information%20and%20Inference&rft.date=2019&rft.volume=8&rft.issue=4&rft.spage=719-755&rft.epage=719-755&rft.eissn=2049-8764&rft.issn=2049-8764&rft.au=BIGOT,%20J%C3%A9r%C3%A9mie&CAZELLES,%20Elsa&PAPADAKIS,%20Nicolas&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||