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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (1): 50-62.doi: 10.3969/j.issn.1005-3085.2022.01.004

• • 上一篇    下一篇

基于无标度先验的有向无环图结构学习

苏温庆,   郭  骁,   张  海   

  1. 西北大学数学学院，西安 710127
  • 出版日期:2022-02-15 发布日期:2022-04-15
  • 基金资助:
    国家自然科学基金 (11571011).

Structure Learning of Directed Acyclic Graphs Incorporating the Scale-free Prior

SU Wenqing,   GUO Xiao,   ZHANG Hai   

  1. School of Mathematics, Northwest University, Xi'an 710127
  • Online:2022-02-15 Published:2022-04-15
  • Supported by:
    The National Natural Science Foundation of China (11571011).

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摘要：

图模型是一种分析网络结构的有效方法，其中有向无环图由于可表示因果关系而受到广泛关注。而大量真实网络中节点的度服从幂律分布，即具有无标度特征。因此，研究了在无标度先验下，节点序已知的有向无环图结构学习问题。通过引入网络中节点度的信息和边的稀疏先验，提出罚项为 Log 型与 $l_q (0<q<1)$ 型惩罚函数复合的正则化模型，通过重赋权迭代算法求解该非凸模型，并分析了算法的收敛性。实验表明，对于模拟数据和真实数据，所提方法均有良好的网络结构学习能力。

关键词: 有向无环图, 无标度, 重赋权迭代

Abstract:

Graphical model is an effective method to analyze the network structure, in which directed acyclic graphs have been widely used to model the causal relationships among variables. While many real networks are scale-free, that is, the degree of the network follows a power-law. The paper considers the problem of structure learning in directed acyclic graphs incorporating the scale-free prior. Specifically, we assume the order of nodes is known in advance. To capture the scale-free property, we propose a novel regularization model with a penalty which is the composite of the Log-type and $l_q (0<q<1)$-type penalty functions to solve the non-convex model and to analyze the convergence of the algorithm. Experiments show that the proposed method performs well for both the simulation study and real data applications. 

Key words: directed acyclic graphs, scale-free, iterative reweighted

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