Chen Jie, Shimmura Ryosuke, Suzuki Joe
Graduate School of Engineering Science, Osaka University, Osaka 560-0043, Japan.
Entropy (Basel). 2021 Dec 2;23(12):1623. doi: 10.3390/e23121623.
We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.
我们将学习视为从稀疏数据中构建的无向图模型。虽然已经提出了几种用于图套索（GL）的高效算法，但交替方向乘子法（ADMM）是处理联合图套索（JGL）的主要方法。我们针对JGL提出了带有和不带有回溯选项的近端梯度算法。这些算法是一阶方法且相对简单，子问题能够以封闭形式高效求解。我们进一步证明了JGL问题解的有界性以及算法中的迭代序列的有界性。数值结果表明，所提出的算法能够实现高精度，并且其效率与现有最先进算法具有竞争力。
