Geodesic
Topics in robust statistical learning
Claire Brecheteau1 ; Edouard Genetay2 ; Timothee Mathieu3 ; Adrien Saumard4
1Univ. Rennes 2, Rennes, France
2CREST, ENSAI, Univ. Rennes, LumenAI, Tours, France
3INRIA, Scool team. Univ. Lille, CRIStAL, CNRS, France
4CREST, 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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     title = {Topics in robust statistical learning},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202374119/}
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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

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