IEEE Trans Neural Netw Learn Syst. 2015 Nov;26(11):2606-20. doi: 10.1109/TNNLS.2014.2384201. Epub 2015 Mar 4.
We consider joint learning of multiple sparse matrix Gaussian graphical models and propose the joint matrix graphical Lasso to discover the conditional independence structures among rows (columns) in the matrix variable under distinct conditions. The proposed approach borrows strength across the different graphical models and is based on the maximum likelihood with penalized row and column precision matrices, respectively. In particular, our model is more parsimonious and flexible than the joint vector graphical models. Furthermore, we establish the asymptotic properties of our model on consistency and sparsistency. And the asymptotic analysis shows that our model enjoys a better convergence rate than the joint vector graphical models. Extensive simulation experiments demonstrate that our methods outperform state-of-the-art methods in identifying graphical structures and estimating precision matrices. Moreover, the effectiveness of our methods is also illustrated via a real data set analysis. Sparsistency is shorthand for consistency of the sparsity pattern of the parameters.
我们考虑联合学习多个稀疏矩阵高斯图模型，并提出联合矩阵图拉索（joint matrix graphical Lasso）来发现矩阵变量中不同条件下行（列）之间的条件独立性结构。所提出的方法在不同的图模型之间借用了优势，并且分别基于惩罚行和列精度矩阵的最大似然。具体来说，我们的模型比联合向量图模型更简约和灵活。此外，我们在一致性和稀疏性上建立了我们模型的渐近性质。渐近分析表明，我们的模型比联合向量图模型具有更好的收敛速度。广泛的模拟实验表明，我们的方法在识别图形结构和估计精度矩阵方面优于最先进的方法。此外，通过对真实数据集的分析也说明了我们方法的有效性。稀疏性是参数稀疏模式一致性的缩写。
