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

Organisateur(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

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

7 21

Bayesian nonparametric estimation of a density living near an unknown manifold

De 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)

Informations sur la vidéo

Date de captation 05/10/2022
Date de publication 03/05/2024
Institut IHP
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Alexandre Duplessis, Marco Perez
Format MP4
Lieu Amphitheater Hermite, IHP

Données de citation

DOI 10.57987/IHP.2022.T3.WS1.007
Citer cette vidéo 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