摘要
有向无环图因果关系的推理是一个重要又具有挑战性的问题。可微因果发现是解决该问题的一种有效方法,但在面对大规模变量时性能较差。为此,提出一种改进的可微因果发现框架,结合了矩阵分解和谱半径的优势。首先,从观测数据中估计协方差矩阵,通过对协方差矩阵分解出有向无环图的可行解;其次,引入谱半径作为无环性约束,提出一种两阶段优化训练过程得到最终的有向无环图。面向几百个变量的稀疏图的实验表明,所提方法相较于次优算法,结构汉明距离下降17%、运行速度提升26%,可扩展到数千个变量,在许多领域具有应用价值。
The inference of causal relationships in directed acyclic graphs is an important and challenging problem.Differentiable causal discovery is an effective method for solving this problem,but its performance is poor when facing large-scale variables.To this end,an improved differentiable causal discovery framework is proposed,which combines the advantages of matrix factorization and spectral radius.Firstly,estimate the covariance matrix from the observed data and decompose it into feasible solutions for the directed acyclic graph;Secondly,introducing spectral radius as an acyclic constraint,a two-stage optimization training process is proposed to obtain the final directed acyclic graph.Experiments on sparse graphs with hundreds of variables show that the proposed method reduces the Hamming distance by 17%and improves the running speed by 26%compared to suboptimal algorithms.It can be extended to thousands of variables and has practical value in many related fields.
作者
田芳文
单剑锋
杨立军
TIAN Fangwen;SHAN Jianfeng;YANG Lijun(College of Electronic and Optical Engineering,Nanjing University of Posts and Telecommunications;Education Quality Monitoring and Evaluation Center,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)
出处
《软件导刊》
2025年第9期82-86,共5页
Software Guide
基金
国家社会科学基金项目(22BTJ030)。
关键词
有向无环图
可微因果发现
矩阵分解
谱半径
directed acyclic graph
differentiable causal discovery
matrix decomposition
spectral radius
