Estimation of Differential Graphs via Log-Sum Penalized D-Trace Loss
Estimation of Differential Graphs via Log-Sum Penalized D-Trace Loss
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DOI：
10.1109/ssp53291.2023.10208014
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发表时间：
2023-07
期刊：
影响因子：
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通讯作者：
Jitendra Tugnait
中科院分区：
文献类型：
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作者：
Jitendra Tugnait
我们考虑的问题，估计两个高斯图形模型（GGM）的差异，这是已知的具有相似的结构。GGM结构被编码在其精度（逆协方差）矩阵中。在许多应用中，人们感兴趣的是估计两个精度矩阵的差异，以表征两组数据的条件依赖性的潜在变化。现有的大多数差分图估计方法都是基于Lasso惩罚损失函数。在本文中，我们分析了一个对数和惩罚的D-跟踪损失函数方法的微分图学习。提出了一种交替方向乘子法（ADMM）优化目标函数。理论分析建立在高维设置的一致性估计。我们说明了我们的方法使用一个数值例子，对数和惩罚D-跟踪损失显着优于激光惩罚D-跟踪损失以及平滑裁剪绝对偏差（SCAD）惩罚D-跟踪损失。
We consider the problem of estimating differences in two Gaussian graphical models (GGMs) which are known to have similar structure. The GGM structure is encoded in its precision (inverse covariance) matrix. In many applications one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data. Most existing methods for differential graph estimation are based on a lasso penalized loss function. In this paper, we analyze a log-sum penalized D-trace loss function approach for differential graph learning. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. Theoretical analysis establishing consistency in estimation in high-dimensional settings is provided. We illustrate our approach using a numerical example where log-sum penalized D-trace loss significantly outperforms lasso-penalized D-trace loss as well as smoothly clipped absolute deviation (SCAD) penalized D-trace loss.