Beyond Lasso: A Survey of Nonconvex Regularization in Gaussian Graphical Models
Beyond Lasso: A Survey of Nonconvex Regularization in Gaussian Graphical Models
复制标题
超越套索：高斯图模型中非凸正则化的调查
DOI：
--
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Williams Dr
中科院分区：
文献类型：
--
作者：
Williams Dr
研究多元数据集中的复杂关系是心理科学中的一项常见任务。近年来，高斯图模型成为描述随机变量条件依赖结构的一种流行模型。虽然图形套索（$ell_1$-正则化）是科学界最著名的估计器，但它有几个缺点，使其不太适合模型选择。现在有专门为克服$ell_1$-罚分固有的问题而开发的正则化的替代形式。本文提供了一个全面的调查非凸正则化，从光滑剪切绝对偏差惩罚的连续近似的$ell_0$-惩罚（即，最佳子集），用于直接估计逆协方差矩阵。这些惩罚共享的一个共同点是，它们都享有Oracle属性，也就是说，它们的执行就像预先知道的生成模型一样。为了确保它们的理论特性是通用的，我进行了大量的数值实验，分别与glasso和非正则化模型选择相比，表明它们具有上级和竞争性的性能，同时对许多变量都是计算可行的。此外，还对正则化模型中的调节参数选择和统计推断等重要问题进行了综述，并将惩罚用于创伤后应激障碍症状的依赖结构估计。讨论包括未来研究的几个想法，包括大量的信息，以促进他们的研究。我已经实现了
Studying complex relations in multivariate datasets is a common task in psychological science. Recently, the Gaussian graphical model has emerged as an increasingly popular model for characterizing the conditional dependence structure of random variables. Although the graphical lasso ($ell_1$-regularization) is the most well-known estimator across the sciences, it has several drawbacks that make it less than ideal for model selection. There are now alternative forms of regularization that were developed specifically to overcome issues inherent to the $ell_1$-penalty.To date, this information has not been synthesized. This paper provides a comprehensive survey of nonconvex regularization that spans from the smoothly clipped absolute deviation penalty to continuous approximations of the $ell_0$-penalty (i.e., best subset) for directly estimating the inverse covariance matrix. A common thread shared by these penalties is that they all enjoy the oracle properties, that is, they perform as though the emph{true} generating model were known in advance. To ensure their theoretical properties are general, I conducted extensive numerical experiments that indicated superior and more than competitive performance when compared to glasso and non-regularized model selection, respectively, all the while being computationally feasible for many variables. In addition, the important topics of tuning parameter selection and statistical inference in regularized models are reviewed.The penalties are employed to estimate the dependence structure of post-traumatic stress disorder symptoms. The discussion includes several ideas for future research, including a plethora of information to facilitate their study. I have implemented the methods in the