CIRM - Videos & books Library - Bayesian spatial adaptation

Virtualconference

Auteurs : Rockova, Veronika (Auteur de la conférence)
CIRM (Editeur )

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Résumé : This paper addresses the following question: “Can regression trees do what other machine learning methods cannot?” To answer this question, we consider the problem of estimating regression functions with spatial inhomogeneities. Many real life applications involve functions that exhibit a variety of shapes including jump discontinuities or high-frequency oscillations. Unfortunately, the overwhelming majority of existing asymptotic minimaxity theory (for density or regression function estimation) is predicated on homogeneous smoothness assumptions which are inadequate for such data. Focusing on locally Holder functions, we provide locally adaptive posterior concentration rate results under the supremum loss. These results certify that trees can adapt to local smoothness by uniformly achieving the point-wise (near) minimax rate. Such results were previously unavailable for regression trees (forests). Going further, we construct locally adaptive credible bands whose width depends on local smoothness and which achieve uniform coverage under local self-similarity. Unlike many other machine learning methods, Bayesian regression trees thus provide valid uncertainty quantification. To highlight the benefits of trees, we show that Gaussian processes cannot adapt to local smoothness by showing lower bound results under a global estimation loss. Bayesian regression trees are thus uniquely suited for estimation and uncertainty quantification of spatially inhomogeneous functions.

Codes MSC :
62G15 - Tolerance and confidence regions
62G20 - Nonparametric asymptotic efficiency

Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/luminy.pdf

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-06-09_Rockova.mp4

Informations sur la Rencontre

Nom de la Rencontre : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Organisateurs de la Rencontre : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Dates : 15/06/2020 - 19/06/2020
Année de la rencontre : 2020
URL de la Rencontre : https://www.cirm-math.com/cirm-virtual-...

Données de citation

DOI : 10.24350/CIRM.V.19642503
Citer cette vidéo: Rockova, Veronika (2020). Bayesian spatial adaptation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19642503
URI : http://dx.doi.org/10.24350/CIRM.V.19642503

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Bibliographie

CASTILLO, Ismael et ROCKOVA, Veronika. Multiscale Analysis of Bayesian CART. University of Chicago, Becker Friedman Institute for Economics Working Paper, 2019, no 2019-127. - https://ssrn.com/abstract=3472021

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