Semi-analytic approximate stability selection for correlated data in generalized linear models
Semi-analytic approximate stability selection for correlated data in generalized linear models
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DOI：
10.1088/1742-5468/ababff
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
Takashi Takahashi;Y. Kabashima
中科院分区：
文献类型：
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作者：
Takashi Takahashi;Y. Kabashima
我们考虑广义线性模型（GLM）的变量选择问题。稳定性选择（SS）是为解决该问题而提出的一种有前景的方法。尽管 SS 提供了实用的变量选择标准，但它的计算要求很高，因为它需要将 GLM 拟合到许多重新采样的数据集。我们提出了一种新颖的近似推理算法，无需重复拟合即可进行 SS。该算法基于统计力学的复制方法和信息论的向量近似消息传递。对于以旋转不变矩阵系综为特征的数据集，我们推导了状态演化方程，宏观地描述了所提出算法的动力学。我们还表明它们的不动点与通过复制方法获得的复制对称解一致。数值实验表明，该算法对合成数据和真实数据都表现出快速收敛和高逼近精度。
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.