Adaptive Bayesian SLOPE—High-dimensional Model Selection with Missing Values

Wei Jiang (1, 2) , Malgorzata Bogdan (3, 4) , Julie Josse (1, 2) , Blazej Miasojedow (5) , Veronika Rockova (6)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 XPOP - Modélisation en pharmacologie de population
3 Faculty of Pure and Applied Mathematics [Wrocław]
4 Skane University Hospital [Lund]
5 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
6 University of Chicago

We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure -- adaptive Bayesian SLOPE -- which effectively combines the SLOPE method (sorted l1 regularization) together with the Spike-and-Slab LASSO method. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation, despite the missing values. As with the Spike-and-Slab LASSO, the coefficients are regarded as arising from a hierarchical model consisting of two groups: (1) the spike for the inactive and (2) the slab for the active. However, instead of assigning independent spike priors for each covariate, here we deploy a joint "SLOPE" spike prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. Through extensive simulations, we demonstrate satisfactory performance in terms of power, FDR and estimation bias under a wide range of scenarios. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent a severe trauma, where we show excellent performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into an R package ABSLOPE for public use.

Mots clés: incomplete data; FDR control; penalized regression; spike and slab prior; stochastic approximation EM; health data

Domaines: Statistiques [stat]; Méthodologie [stat.ME]

Wei Jiang, Malgorzata Bogdan, Julie Josse, Blazej Miasojedow, Veronika Rockova. Adaptive Bayesian SLOPE—High-dimensional Model Selection with Missing Values. 2020. ⟨hal-02430600⟩