偏相关图形套索（partial correlation graphical lasso）的存在性与优化
Existence and optimisation of the partial correlation graphical lasso
AI总结：
针对偏相关图形套索（PCGLASSO）的非凸优化计算难题，证明其在样本量小于维度时估计量存在，提出交替算法并推出首个公开R实现，在中等维度下计算效率具竞争力。
摘要：
偏相关图形套索（PCGLASSO）是一种面向高斯图模型的惩罚似然方法，可实现精度矩阵的尺度不变稀疏估计，是对流行的图形套索（graphical LASSO）方法的改进。然而，由于其相关优化问题具有非凸性，PCGLASSO 面临计算层面的挑战。本文在 PCGLASSO 的计算方面取得了若干重要突破。首先，本文证明了当样本量小于维度时（即最大似然估计不存在的情形），PCGLASSO 估计量是存在的，这意味着 PCGLASSO 可适用于任意高斯数据。其次，本文提出了一种用于计算 PCGLASSO 的新型交替算法，并在 R 包 PCGLASSO 中实现，该包可在 https://github.com/JackStorrorCarter/PCGLASSO 获取。这是首个公开可用的 PCGLASSO 实现，在中等维度规模下具备具备竞争力的计算速度。
英文摘要：
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.
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