论文标题
在广义线性模型中相关数据的半分析近似稳定性选择
Semi-analytic approximate stability selection for correlated data in generalized linear models
论文作者
论文摘要
我们考虑广义线性模型（GLM）的可变选择问题。稳定性选择（SS）是提出了解决此问题的有前途的方法。尽管SS提供了实用的可变选择标准，但它在计算上是要求的，因为它需要将GLMS拟合到许多重新采样的数据集中。我们提出了一种新型的近似推理算法，该算法可以在不重复拟合的情况下进行SS。该算法基于统计力学的复制方法和矢量近似信息理论的信息传递。对于以旋转不变矩阵集合为特征的数据集，我们得出了宏观描述所提出算法动力学的状态进化方程。我们还表明，它们的固定点与复制方法获得的副本对称解是一致的。数值实验表明，对于合成和现实世界数据，该算法表现出快速收敛和高近似精度。
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.
