About Event
Given i.i.d. random variables X1,…,Xn ∈ ℝD drawn from a stratified mixture ⋃ k=1KMk of immersed C2-manifolds of different dimensions (dk)k≤K, we study the minimax estimation of the family (Mk)k≤K and the associated unsupervised clustering problem. We provide a constructive algorithm allowing to estimate each mixture component Mk at its optimal dimension-specific rate (log(n)∕n)2∕dk adaptively. The method is based on an ascending hierarchical co-detection of points belonging to different layers which also identifies the number of layers K, the dimensions (dk)k≤K, assign each point Xi to a layer accurately, and estimate tangent spaces optimally. The results hold regardless of any reach assumption on the Mk’s nor on intersection configurations Mk ∩ Mk′ . They open the way to a broad clustering framework, where each mixture component (or stratum) Mk models a cluster, emanating from a specific nonlinear correlation phenomenon leaving only dk local degrees of freedom.
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Apoiadores / Parceiros / Patrocinadores
Speakers
Eddie Aamari
Aamari obtained his Phd in 2017 with the thesis "Rates of convergence for geometric inference", Orsay University, supervised by Pascal Massart and Frédéric Chazal. He is CNRS researcher since 2017. In 2018-2023 he was in Sorbonne Université and Université Paris Cité. Since 2023 he is at ENS Paris (École normale supérieure).
Location
Endereço
a) Opção presencial *
Praia de Botafogo, 190
5o andar, Auditório 537
b) Opção remota (via Zoom)
Link: ID: 95348442773
Informações adicionais:
Tel: 55 21 3799-5917