多重高斯有向图模型结构学习

THE STRUCTURE LEARNING OF MULTIPLE GAUSSIAN DIRECED GRAPHS

对k个节点数为n的高斯有向图,本文充分利用节点之间的偏序先验,并挖掘多重高斯有向图之间的相似性结构,并将其分为p个组.基于极大似然估计提出了带相似性结构惩罚项的Lasso回归模型用于估计图的邻接矩阵,并利用时间复杂度为O(nk^2p)的坐标下降法求解该模型.通过数值实验对比了本文算法和PC算法,证明了本文算法较PC算法对于多重高斯有向图具有较好地恢复效果.

In this paper, we fully utilize the natural ordering between nodes and use the similarity structure between different graphs. A regression model based on the maximum likelihood estimation with similar structure penalty term is proposed to estimate the adjacency matrices of the networks . Computationally, the model is solved by coordinate descent method with complexity O(nk^2p). Compared with PC algorithm, numerical experiments demonstrates the algorithm proposed in this paper performs well.