Abstract
We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is computationally demanding because it needs to fit GLMs to many re-sampled datasets. We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting. The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory. For datasets characterized by rotation-invariant matrix ensembles, we derive state evolution equations that macroscopically describe the dynamics of the proposed algorithm. We also show that their fixed points are consistent with the replica symmetric solution obtained by the replica method. Numerical experiments indicate that the algorithm exhibits fast convergence and high approximation accuracy for both synthetic and real-world data.
Highlights
Stability selection (SS) is a promising method proposed for solving this problem
We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting
The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory
Summary
Semi-analytic approximate stability selection for correlated data in generalized linear models E-mail: takahashi.t.cc@m.titech.ac.jp Department of Mathematical and Computing Science Tokyo Institute of Technology 2-12-1, Ookayama, Meguro-ku, Tokyo, Japan
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