CIRM - Videos & books Library - Bayesian spatial adaptation

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Authors : Rockova, Veronika (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

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

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

Information on the Video

Film maker :

Hennenfent, Guillaume

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

Information on the Event

Event Title : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Event Organizers : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Dates : 15/06/2020 - 19/06/2020
Event Year : 2020
Event URL : https://www.cirm-math.com/cirm-virtual-...

Citation Data

DOI : 10.24350/CIRM.V.19642503
Cite this video as: 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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Bibliography

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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