基于机器学习的格兰杰因果网络重构算法研究

The aim of complex network reconstruction is to infer inter-relationships among nodes from real datasets，so as to analyze overall dynamic behavior, structural properties, and influence mechanisms of the networked system. For the nonlinearity, causality and insufficient sample size of data together with temporal and spatial heterogeneity, this project mainly focuses on the Granger causality network reconstruction method based on machine learning. Firstly, the nonlinear modeling of complex networked systems is designed and implemented, and a nonlinear Granger causality network reconstruction method based on Bayesian group-sparse is proposed. Furthermore, the efficiency of large-scale network reconstruction could be improved by parallel computing. Secondly, the Granger causality network reconstruction method based on multi-task learning is given by using prior information of network. Finally, in order to solve the model-dependence of the reconstruction method, the model-free Granger causality network reconstruction method based on multi-classification is proposed. Then directed path consistency algorithm is designed to eliminate the false edges of network. In addition, the problem of network reconstruction with nonuniform lags is considered in the Granger causality method. In this project, nonlinear system modeling, machine learning and other means are used comprehensively, and it is expected to discover network structure by means of function approximation theory, Bayesian theory, multi-classification learning and multi-task learning, so as to provide a new approach and effective algorithm for reconstructing the topology structure of complex networks from massive data.

复杂网络重构旨在基于实际数据去推断网络中节点间的相互作用关系，以便分析系统动力学行为、结构特性和影响机制。本项目针对实际复杂网络中的非线性、因果性及数据样本量不足且存在时空异质性等主要特征，重点研究基于机器学习的格兰杰因果网络重构方法。首先设计实现复杂网络化系统的非线性建模，提出了基于贝叶斯组稀疏的非线性格兰杰因果网络重构方法，再结合并行计算提高大规模网络的重构效率；其次提出了融合先验结构信息的多任务学习格兰杰因果网络重构算法；最后为解决重构算法对模型的依赖性，提出一种无模型的基于多分类格兰杰因果网络重构方法，并设计有向路径一致性算法，消除网络中的虚假连边，另外考虑了格兰杰因果的时滞非均匀嵌入问题。本项目综合运用非线性系统建模和机器学习等手段，期望凭借函数逼近论、贝叶斯理论、多分类学习以及多任务学习等方法去研究复杂的网络关系，为从海量数据中挖掘复杂网络的拓扑结构提供新的途径和有效的算法。

复杂网络重构是分析系统动力学行为、结构特性和影响机制的前提和基础，是近年来网络科学领域研究的一个热点。本项目针对实际复杂网络中的非线性、因果性及稀疏性等主要特征，重点研究基于机器学习的网络重构方法。主要完成了如下子课题：. (1) 提出了一种块正交匹配追踪-非线性条件格兰杰因果(BOMP-NCGC)方法，基于高斯核函数构建非线性条件格兰杰因果关系模型，再结合块正交匹配追踪选择组稀疏变量，并进行后续的因果行分析；. (2) 提出了基于组稀疏惩罚非线性最小二乘方法，基于函数逼近理论和特征选择，通过求解这个稀疏组优化问题，来获得复杂网络化系统的拓扑结构。. (3) 提出了基于条件互信息的集成路径一致性算法(EPCACMI)，首先采用主成分分析，将大规模网络分解成若干个小规模的子网络，然后采用基于条件互信息的路径一致性算法，消除间接关系，接着将所有子网进行整合，获得最终的网络结构。. (4) 提出了基于条件互信息的局部Lasso路径一致性算法（Loc-Lasso-PCACMI），从局部网络推断的角度，集成了Lasso算法和PCACMI的优点，提高了网络重构算法的性能和效率。. (5) 设计了一种基于重采样策略的动态阈值条件互信息算法(DTCMI)，不像传统的相关性算法需要设置固定的阈值，另外使用基于折叠刀的重采样策略，进一步提高了重构网络的精度。. 本项目的仿真研究数据来源主要基于经典的网络化系统模型和基因调控网络数据集（包括DREAM竞赛的数据集）。当今时代，构建准确的基因调控网络已成为近年来生物信息学领域的重要研究课题。因此，尤其是针对基因调控网络的仿真研究，有助于我们分析和理解基因之间的调控机制，进而去揭示一些复杂的生物现象。

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