广义线性模型中相关数据的半解析近似稳定性选择
Semi-analytic approximate stability selection for correlated data in generalized linear models
AI总结：
针对广义线性模型变量选择中稳定性选择计算成本高的问题，提出基于复制方法与向量近似消息传递的近似推断算法，实现无需重复拟合的稳定性选择，并在旋转不变矩阵系综下推导状态演化方程，实验验证其快速收敛和高精度。
摘要：
我们考虑广义线性模型（GLMs）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，但由于需要对许多重采样数据集拟合GLM，其计算需求很高。我们提出了一种新颖的近似推断算法，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（replica method）和信息论的向量近似消息传递（vector approximate message passing）。对于由旋转不变矩阵系综表征的数据集，我们推导了状态演化方程，该方程宏观地描述了所提出算法的动态行为。我们还证明了它们的固定点与通过复制方法获得的复制对称解一致。数值实验表明，该算法在合成数据和真实数据上均表现出快速收敛性和高近似精度。
英文摘要：
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.
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