CIRM - Videos & books Library - Floodgate: inference for model-free variable importance

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Auteurs : Janson, Lucas (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : Many modern applications seek to understand the relationship between an outcome variable of interest and a high-dimensional set of covariates. Often the first question asked is which covariates are important in this relationship, but the immediate next question, which in fact subsumes the first, is \emph{how} important each covariate is in this relationship. In parametric regression this question is answered through confidence intervals on the parameters. But without making substantial assumptions about the relationship between the outcome and the covariates, it is unclear even how to \emph{measure} variable importance, and for most sensible choices even less clear how to provide inference for it under reasonable conditions. In this paper we propose \emph{floodgate}, a novel method to provide asymptotic inference for a scalar measure of variable importance which we argue has universal appeal, while assuming nothing but moment bounds about the relationship between the outcome and the covariates. We take a model-X approach and thus assume the covariate distribution is known, but extend floodgate to the setting that only a \emph{model} for the covariate distribution is known and also quantify its robustness to violations of the modeling assumptions. We demonstrate floodgate's performance through extensive simulations and apply it to data from the UK Biobank to quantify the effects of genetic mutations on traits of interest.

Keywords : Variable importance; effect size; model-X; heterogeneous treatment effects; heritability

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

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

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-06-05_Janson.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 Congrès : https://www.cirm-math.com/cirm-virtual-...

Données de citation

DOI : 10.24350/CIRM.V.19641303
Citer cette vidéo: Janson, Lucas (2020). Floodgate: inference for model-free variable importance. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19641303
URI : http://dx.doi.org/10.24350/CIRM.V.19641303

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Bibliographie

BERK, Richard, BROWN, Lawrence, BUJA, Andreas, et al. Valid post-selection inference. The Annals of Statistics, 2013, vol. 41, no 2, p. 802-837. - http://dx.doi.org/10.1214/12-AOS1077

BÜHLMANN, Peter, et al. Statistical significance in high-dimensional linear models. Bernoulli, 2013, vol. 19, no 4, p. 1212-1242. - http://dx.doi.org/10.3150/12-BEJSP11

BÜHLMANN, Peter, VAN DE GEER, Sara, et al. High-dimensional inference in misspecified linear models. Electronic Journal of Statistics, 2015, vol. 9, no 1, p. 1449-1473. - http://dx.doi.org/10.1214/15-EJS1041

BUJA, Andreas, BERK, Richard A., BROWN, Lawrence D., et al. Models as approximations-a conspiracy of random regressors and model deviations against classical inference in regression. Statistical Science, 2015, p. 1. - https://crim.sas.upenn.edu/sites/default/files/2015-9.0_Berk_ModelsAsApproximations%281%29.pdf

BUJA, Andeas et BROWN, Larry. Discussion:" a significance test for the lasso". The Annals of Statistics, 2014, vol. 42, no 2, p. 509-517. - http://dx.doi.org/10.1214/14-AOS1175F

BUJA, Andreas, BROWN, Lawrence, BERK, Richard, et al. Models as Approximations I: Consequences Illustrated with Linear Regression. Statistical Science, 2019, vol. 34, no 4, p. 523-544. - http://dx.doi.org/10.1214/18-STS693

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