发表机构
Vanderbilt University; The Pennsylvania State University（范德堡大学; 宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高斯图模型边选择中固定正则化参数不适应数据的问题，提出基于极值理论的数据自适应惩罚族，通过290个数据集和模拟验证，在保持特异性的同时提高敏感性，推荐Weibull惩罚。
AI 中文摘要
在高斯图模型中，边选择本质上是一个变量选择问题，其中成对关系决定了心理网络中构念效度和变量重要性。在心理学中，网络估计主要依赖于ℓ1正则化，其均匀收缩系统地低估了边和中心性参数。其他惩罚方法虽克服了这种偏差，但依赖于固定的超参数，无法适应数据中的信号。我们开发了一族基于极值理论的数据自适应正则化惩罚。通过对290个实证心理数据集的分析，我们表明绝对偏相关系数能很好地由Weibull分布描述。利用这一经验规律，我们推导出Weibull、Gumbel和Exponential惩罚，它们近似ℓ0惩罚，并将其超参数校准到每个数据集的噪声底限。我们正式证明了其静态形式的渐近性质，并进行了涵盖两种网络拓扑和多种样本量（N=100–10,000）的大规模模拟，表明其自适应形式在保持高特异性的同时，随着样本量的增加累积敏感性，且参数偏差低，与领域标准相比具有高秩序中心性一致性。实证上，在心理学典型的样本量下，仅方法选择就决定了中心性排名。在三种自适应惩罚中，鉴于其参数的可解释性，推荐使用Weibull。
英文摘要
Edge selection in Gaussian graphical models is fundamentally a variable selection problem where pairwise relationships determine construct validity and variable importance in psychological networks. In psychology, network estimation relies predominantly on \(\ell_1\) regularization where uniform shrinkage systematically underestimates edge and centrality parameters. Alternative penalties overcome this bias but rely on fixed hyperparameters that do not adapt to the signal in the data. We develop a family of data-adaptive regularization penalties grounded in extreme value theory. Across 290 empirical psychological datasets, we show that absolute partial correlations are well-described by the Weibull distribution. Using this empirical regularity, we derive Weibull, Gumbel, and Exponential penalties that approximate \(\ell_0\) penalization and calibrate their hyperparameters to each dataset's noise floor. We formally prove the asymptotic properties of their static forms and conduct a large-scale simulation spanning two network topologies and various sample sizes (\(N\) = 100--10,000), demonstrating that their adaptive forms maintain high specificity while accumulating sensitivity as sample size increases with low parameter bias and high rank-order centrality congruence relative to field standards. Empirically, method choice alone determined centrality rankings at sample sizes typical in psychology. Of the three adaptive penalties, Weibull is recommended given the interpretability of its parameters.
Comments18 pages, 4 figures, 6 appendices
