LARGE：一种用于估计高斯图模型的局部自适应正则化方法
LARGE: A Locally Adaptive Regularization Approach for Estimating Gaussian Graphical Models
AI总结：
LARGE通过自适应学习节点层面的正则化参数，提高高斯图模型的估计和选择精度，尤其在处理异质性fMRI数据时表现优异。
摘要：
图Lasso（GLASSO）是一种广泛用于学习高维无向高斯图模型（GGM）的算法。给定来自多元正态分布的i.i.d.观测值，GLASSO通过最大化对数似然函数并施加对非对角线元素的\ell_1惩罚来估计精度矩阵。然而，在这种无监督设置中选择最优正则化参数λ仍是一个重大挑战。已知的问题是，现有方法如离样似然最大化会选择一个单一的全局λ，而不考虑变量缩放或部分方差的异质性。将数据标准化为单位方差，虽然是一种常见的 workaround，但已被证明会负面影响图恢复。在图估计中解决节点层面的自适应调参问题对于应用如计算神经科学至关重要，其中脑网络是从高度异质性的、区域特定的fMRI数据中构建的。在本工作中，我们开发了用于图估计的局部自适应正则化（LARGE），一种自适应学习节点层面调参以提高图估计和选择的方法。在GLASSO的每个块坐标下降步骤中，我们扩展了节点层面的Lasso回归，以联合估计回归系数和误差方差，这反过来又指导了节点层面惩罚的自适应学习。在模拟中，LARGE在图恢复方面始终优于基准方法，展示了在多次重复中更大的稳定性，并在最困难的模拟设置中实现了最佳的估计准确性。我们通过从真实fMRI数据集中估计脑功能连接性来展示我们方法的实用价值。
英文摘要：
The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by maximizing the log-likelihood with an \ell_1-penalty on the off-diagonal entries. However, selecting an optimal regularization parameter λin this unsupervised setting remains a significant challenge. A well-known issue is that existing methods, such as out-of-sample likelihood maximization, select a single global λand do not account for heterogeneity in variable scaling or partial variances. Standardizing the data to unit variances, although a common workaround, has been shown to negatively affect graph recovery. Addressing the problem of nodewise adaptive tuning in graph estimation is crucial for applications like computational neuroscience, where brain networks are constructed from highly heterogeneous, region-specific fMRI data. In this work, we develop Locally Adaptive Regularization for Graph Estimation (LARGE), an approach to adaptively learn nodewise tuning parameters to improve graph estimation and selection. In each block coordinate descent step of GLASSO, we augment the nodewise Lasso regression to jointly estimate the regression coefficients and error variance, which in turn guides the adaptive learning of nodewise penalties. In simulations, LARGE consistently outperforms benchmark methods in graph recovery, demonstrates greater stability across replications, and achieves the best estimation accuracy in the most difficult simulation settings. We demonstrate the practical utility of our method by estimating brain functional connectivity from a real fMRI data set.
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