Geodesic
Topics in robust statistical learning
Claire Brecheteau1 ; Edouard Genetay2 ; Timothee Mathieu3 ; Adrien Saumard4
1 Univ. Rennes 2, Rennes, France
2 CREST, ENSAI, Univ. Rennes, LumenAI, Tours, France
3 INRIA, Scool team. Univ. Lille, CRIStAL, CNRS, France
4 CREST, ENSAI, Univ. Rennes, Bruz, France
ESAIM. Proceedings, Tome 74 (2023), pp. 119-136.

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Some recent contributions to robust inference are presented. Firstly, the classical problem of robust M-estimation of a location parameter is revisited using an optimal transport approach - with specifically designed Wasserstein-type distances - that reduces robustness to a continuity property. Secondly, a procedure of estimation of the distance function to a compact set is described, using union of balls. This methodology originates in the field of topological inference and offers as a byproduct a robust clustering method. Thirdly, a robust Lloyd-type algorithm for clustering is constructed, using a bootstrap variant of the median-of-means strategy. This algorithm comes with a robust initialization.
DOI : 10.1051/proc/202374119

Claire Brecheteau 1 ; Edouard Genetay 2 ; Timothee Mathieu 3 ; Adrien Saumard 4

1 Univ. Rennes 2, Rennes, France
2 CREST, ENSAI, Univ. Rennes, LumenAI, Tours, France
3 INRIA, Scool team. Univ. Lille, CRIStAL, CNRS, France
4 CREST, ENSAI, Univ. Rennes, Bruz, France 
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Claire Brecheteau; Edouard Genetay; Timothee Mathieu; Adrien Saumard. Topics in robust statistical learning. ESAIM. Proceedings, Tome 74 (2023), pp. 119-136. doi : 10.1051/proc/202374119. http://geodesic.mathdoc.fr/articles/10.1051/proc/202374119/

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