We consider learning 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 for joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order 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 iterations 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.

翻译：我们考虑从稀少的数据中学习一个非方向图形模型。 虽然已经为图形拉索(GL)提出了几种高效的算法,但乘数交替方向法(ADMM)是用于联合图形拉索(JGL)的主要方法。我们为JGL提出了有和没有回溯选择的近似渐变程序。这些程序是第一阶和相对简单的,而次级问题以封闭的形式得到了有效的解决。我们进一步显示了JGL问题解决方案的界限和算法中的迭代。数字结果显示,提议的算法可以达到高度的准确性和精确性,其效率与最新算法具有竞争力。