Collection 2022 - T3 - WS1 - Non-Linear and High Dimensional Inference

Organizer(s) Aamari, Eddie ; Aaron, Catherine ; Chazal, Frédéric ; Fischer, Aurélie ; Hoffmann, Marc ; Le Brigant, Alice ; Levrard, Clément ; Michel, Bertrand

Date(s) 03/10/2022 - 07/10/2022

linked URL https://indico.math.cnrs.fr/event/7545/

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Bayesian nonparametric estimation of a density living near an unknown manifold

By Judith Rousseau

In high dimensions it is common to assume that the data have a lower dimensional structure. In this work we consider that the observations are iid and with a distribution whose support is concentrated near a lower dimensional manifold. Neither the manifold nor the density is known. A typical example is for noisy observations on an unknown low dimensional manifold. We consider a family of Bayesian nonparametric density estimators based on location -scale Gaussian mixture priors and we study the asymptotic properties of the posterior distribution. Our work shows in particular that non conjuguate location -scale Gaussian mixture models can adapt to complex geometries and spatially varying regularity. This talk will also review the various aspects of mixtures of Gaussian for density estimation. (Joint work with Clément Berenfeld, Dauphine, and Paul Rosa, Oxford)

Information about the video

Date of recording 05/10/2022
Date of publication 16/04/2024
Institution IHP
Language English
Audience Researchers, Graduate Students
Director(s) Alexandre Duplessis, Marco Perez
Format MP4
Venue Amphitheater Hermite, IHP

Citation data

DOI 10.57987/IHP.2022.T3.WS1.007
Cite this video Rousseau, Judith (05/10/2022). Bayesian nonparametric estimation of a density living near an unknown manifold. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T3.WS1.007
URL https://dx.doi.org/10.57987/IHP.2022.T3.WS1.007