Semi-analytic approximate stability selection for correlated data in generalized linear models
This work addresses a computational bottleneck for researchers and practitioners using stability selection in high-dimensional data analysis, though it is incremental as it builds on existing methods.
The authors tackled the computational burden of stability selection for variable selection in generalized linear models by proposing a novel approximate inference algorithm that avoids repeated model fitting, achieving fast convergence and high accuracy in synthetic and real-world data.
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.