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Title: Adaptive Bayesian SLOPE: High-dimensional model selection with missing values Authors:  Wei Jiang - Ecole Polytechnique (France)
Malgorzata Bogdan - University of Wroclaw (Poland) [presenting]
Julie Josse - INRIA (France)
Blazej Miasojedow - University of Warsaw (Poland)
Veronika Rockova - University of Chicago (United States)
Abstract: The selection of variables with high-dimensional and missing data is a major challenge and very few methods are available to solve this problem. We propose a method -- adaptive Bayesian SLOPE -- which is an extension of the Sorted L-One Penalized Estimator within a Bayesian framework and which allows us to simultaneously estimate the parameters and select variables for FDR control for large data despite missing values. Extensive simulations highlight the good behavior in terms of power, FDR and estimation bias under a wide range of simulation scenarios. Finally, we consider an application for prediction of the level of platelets for severely traumatized patients from Paris hospitals. We demonstrate that beyond the advantage of selecting relevant variables, which is crucial for interpretation, ABSLOPE has excellent predictive capabilities. The methodology is implemented in the R package ABSLOPE, which incorporates C++ code to improve the efficiency of the proposed method.