C. Brécheteau, Edouard Genetay, Timothee Mathieu, Adrien Saumard
{"title":"Topics in robust statistical learning","authors":"C. Brécheteau, Edouard Genetay, Timothee Mathieu, Adrien Saumard","doi":"10.1051/proc/202374119","DOIUrl":"https://doi.org/10.1051/proc/202374119","url":null,"abstract":"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.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139295014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some recent advances in random walks and random environments","authors":"Alexis Devulder, Roland Diel, Xiaolin Zeng","doi":"10.1051/proc/202374038","DOIUrl":"https://doi.org/10.1051/proc/202374038","url":null,"abstract":"Recent contributions to random walks in random environments and related topics are presented. We focus on non parametric estimation for one dimensional random walks in random environment and on the Dirichlet distribution on decomposable graphs.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139298770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Machine learning and optimal transport: some statistical and algorithmic tools","authors":"Elsa Cazelles","doi":"10.1051/proc/202374158","DOIUrl":"https://doi.org/10.1051/proc/202374158","url":null,"abstract":"In this paper, we focus on the analysis of data that can be described by probability measures supported on a Euclidean space, by way of optimal transport. Our main objective is to present a first and second order statistical analyses in the space of distributions in a concise manner, as a first approach to understand the general modes of variation of a set of observations. In the context of optimal transport, these studies correspond to the barycenter and the decomposition into geodesic principal components in theWasserstein space. In particular, we aim attention at a regularised estimator of the barycenter, in order to handle the noise coming from the observations. Additionally, we leverage these tools for time series analysis, whose spectral informations are compared using optimal transport.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139294266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Wave propagation in random media: beyond Gaussian statistics","authors":"Josselin Garnier","doi":"10.1051/proc/202374063","DOIUrl":"https://doi.org/10.1051/proc/202374063","url":null,"abstract":"In this paper we review some aspects of wave propagation in random media. In the physics literature the picture seems simple: for large propagation distances, the wavefield has Gaussian statistics, mean zero, and second-order moments determined by radiative transfer theory. The results for the first two moments can be proved under general circumstances by multiscale analysis. The Gaussian conjecture for the statistical distribution of the wavefield can be proved in some propagation regimes, such as the white-noise paraxial regime that we address in the first part of this review. It may, however, be wrong in other regimes, such as in randomly perturbed open waveguides, that we address in the second part of this review. In the third and last part, we reconcile the two results by showing that the Gaussian conjecture is restored in randomly perturbed open waveguides in the high-frequency regime, when the number of propagating modes increases.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139297695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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