用非凸正则化方法更精准地挖掘多属性图模型间的差异结构。
Learning Multi-Attribute Differential Graphs with Non-Convex Penalties
- 采用非凸惩罚的D-迹损失函数，提升差异图估计精度。
- 在高维情况下实现支持集恢复一致性和参数估计收敛。
- 适合需要精细建模多组数据差异的统计学习研究者。
我们研究在两个具有相似结构的多属性高斯图模型（GGM）之间估计差异的问题，采用带非凸惩罚（log-sum与SCAD）的惩罚D-迹损失函数。GGM的结构由其精度矩阵（逆协方差矩阵）编码。现有方法基于分组Lasso惩罚损失函数。本文提出一种带非凸惩罚的惩罚D-迹损失函数，并设计两种近端梯度下降算法优化目标函数。理论分析给出了高维设定下支持集恢复一致性、凸性及参数估计的一致性条件。通过合成数据和真实数据的数值实验验证了方法的有效性。
原文摘要 · Abstract (English)
We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with non-convex penalties. The GGM structure is encoded in its precision (inverse covariance) matrix. Existing methods for multi-attribute differential graph estimation are based on a group lasso penalized loss function. In this paper, we consider a penalized D-trace loss function with non-convex (log-sum and smoothly clipped absolute deviation (SCAD)) penalties. Two proximal gradient descent methods are presented to optimize the objective function. Theoretical analysis establishing sufficient conditions for consistency in support recovery, convexity and estimation in high-dimensional settings is provided. We illustrate our approaches with numerical examples based on synthetic and real data.
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