偏相关图套索的存在性与优化 (Existence and optimisation of the partial correlation graphical lasso)

The partial correlation graphical LASSO (PCGLASSO) is a penalised likelihood method for Gaussian graphical models which provides scale invariant sparse estimation of the precision matrix and improves upon the popular graphical LASSO method. However, the PCGLASSO suffers from computational challenges due to the non-convexity of its associated optimisation problem. This paper provides some important breakthroughs in the computation of the PCGLASSO. First, the existence of the PCGLASSO estimate is proven when the sample size is smaller than the dimension - a case in which the maximum likelihood estimate does not exist. This means that the PCGLASSO can be used with any Gaussian data. Second, a new alternating algorithm for computing the PCGLASSO is proposed and implemented in the R package PCGLASSO available at https://github.com/JackStorrorCarter/PCGLASSO. This was the first publicly available implementation of the PCGLASSO and provides competitive computation time for moderate dimension size.

翻译：偏相关图套索（PCGLASSO）是一种用于高斯图模型的惩罚似然方法，它提供了精度矩阵的尺度不变稀疏估计，并改进了流行的图套索方法。然而，由于相关优化问题的非凸性，PCGLASSO面临计算挑战。本文在PCGLASSO的计算方面取得了一些重要突破。首先，证明了当样本量小于维度时PCGLASSO估计的存在性——在这种情况下最大似然估计不存在。这意味着PCGLASSO可用于任何高斯数据。其次，提出了一种计算PCGLASSO的新交替算法，并在R包PCGLASSO中实现，该包可从https://github.com/JackStorrorCarter/PCGLASSO获取。这是首个公开可用的PCGLASSO实现，在中等维度规模下提供了具有竞争力的计算时间。