基于因果发现的复杂系统根因分析方法综述

doi:10.12305/j.issn.1001-506X.2025.10.19

系统工程与电子技术 ›› 2025, Vol. 47 ›› Issue (10): 3325-3352.doi: 10.12305/j.issn.1001-506X.2025.10.19

• 系统工程 • 上一篇

基于因果发现的复杂系统根因分析方法综述

朱晓敏¹(), 陶晶晶²(), 马力¹^,*(), 刘春龙³(), 王顺鸽³(), 薛依玲³(), 于沂渭³(), 林澈³(), 李文姬³(), 庄嘉帆³(), 徐标³(), 范衠⁴()

1. 军事科学院战略评估咨询中心，北京 100091
2. 国防科技大学计算机学院，湖南长沙 410073
3. 汕头大学工学院，广东汕头 515063
4. 电子科技大学（深圳）高等研究院，广东深圳 518110

收稿日期:2024-06-28 出版日期:2025-10-25 发布日期:2025-10-23
通讯作者: 马力 E-mail:xmzhu@nudt.edu.cn;taojingjing_nudt@163.com;18874857546@163.com;22clliu@stu.edu.cn;22sgwang@stu.edu.cn;22ylxue@stu.edu.cn;21yyyu@stu.edu.cn;19clin1@stu.edu.cn;liwj@stu.edu.cn;jfzhuang@stu.edu.cn;xubiao@stu.edu.cn;fanzhun@uestc.edu.cn
作者简介:朱晓敏（1979—），男，研究员，博士，主要研究方向为军事评估、因果推断、数据分析
陶晶晶（1997—），女，博士研究生，主要研究方向为群体智能、因果推断
刘春龙（2000—），男，硕士研究生，主要研究方向为因果推断
王顺鸽（2000—），女，硕士研究生，主要研究方向为因果推断
薛依玲（1998—），女，硕士研究生，主要研究方向为因果推断
于沂渭（1997—），男，硕士研究生，主要研究方向为因果推断
林　澈（2001—），男，硕士研究生，主要研究方向为因果推断、计算机视觉
李文姬（1988—），男，讲师，博士，主要研究方向为计算智能、群体智能、因果推断
庄嘉帆（1994—），男，副研究员，博士，主要研究方向为计算机视觉、机器人感知
徐　标（1981—），男，讲师，博士，主要研究方向为智能优化算法、路径规划、无人机−车辆协同任务分配
范　衠（1974—），男，教授，博士，主要研究方向为人工智能与机器人、群体智能、设计自动化

Survey on root cause analysis methods for complex systems based on causal discovery

Xiaomin ZHU¹(), Jingjing TAO²(), Li MA¹^,*(), Chunlong LIU³(), Shunge WANG³(), Yiling XUE³(), Yiwei YU³(), Che LIN³(), Wenji LI³(), Jiafan ZHUANG³(), Biao XU³(), Zhun FAN⁴()

1. Strategic Assessments and Consultation Institute，Academy of Military Sciences，Beijing 100091，China
2. School of Computer Science and Technology，National University of Defense Technology，Changsha 410073，China
3. College of Engineering，Shantou University，Shantou 515063，China
4. Shenzhen Institute of Advanced Study，University of Electronic Science and Technology of China，Shenzhen 518110，China

Received:2024-06-28 Online:2025-10-25 Published:2025-10-23
Contact: Li MA E-mail:xmzhu@nudt.edu.cn;taojingjing_nudt@163.com;18874857546@163.com;22clliu@stu.edu.cn;22sgwang@stu.edu.cn;22ylxue@stu.edu.cn;21yyyu@stu.edu.cn;19clin1@stu.edu.cn;liwj@stu.edu.cn;jfzhuang@stu.edu.cn;xubiao@stu.edu.cn;fanzhun@uestc.edu.cn

摘要/Abstract

摘要：

针对如何选择合适的因果发现方法、计算因果影响强度，并进行精确的根因定位，首先介绍了不同的因果发现方法，并分析其应用于复杂系统的优劣。其次，探讨了因果影响权重的计算方法。再次，对复杂系统的根因定位方法进行了系统概述。接着，归纳了现有研究的应用领域，并列举已有数据集与工具平台。然后，从复杂系统的观测数据处理、因果发现方法设计、根因定位方法设计、根因分析结果评估4个方面提出存在的问题与挑战。最后，从数据处理、因果发现方法、根因定位方法、结果评估与检验4个方面进行展望。本文可为进一步深入探索基于因果发现的复杂系统根因分析提供参考。

关键词: 因果推断, 因果发现, 复杂系统, 根因分析

Abstract:

Aimed at how to select appropriate causal discovery methods, calculate the strength of causal influence, and accurately locate root causes, firstly, different causal discovery methods are introduced, and their advantages and disadvantages are analyzed when applied to complex systems. Secondly, the calculation methods is explored for causal influence weights. Thirdly, a systematic overview of root cause localization methods for complex systems is provided. Next, the application areas of existing research is summarized, and the available datasets and tool platforms are listed. Then, the existing problems and challenges are identified from four aspects: the processing of observational data from complex systems, the design of causal discovery methods, the design of root cause localization methods, and the evaluation of root cause analysis results. Finally, the prospects for future research are provided from four aspects: data processing, causal discovery methods, root cause localization methods, and result evaluation and validation. This paper can serve as a reference for further in-depth exploration of root cause analysis in complex systems based on causal discovery.

Key words: causal inference, causal discovery, complex system, root cause analysis

中图分类号:

TP 182

朱晓敏, 陶晶晶, 马力, 刘春龙, 王顺鸽, 薛依玲, 于沂渭, 林澈, 李文姬, 庄嘉帆, 徐标, 范衠. 基于因果发现的复杂系统根因分析方法综述[J]. 系统工程与电子技术, 2025, 47(10): 3325-3352.

Xiaomin ZHU, Jingjing TAO, Li MA, Chunlong LIU, Shunge WANG, Yiling XUE, Yiwei YU, Che LIN, Wenji LI, Jiafan ZHUANG, Biao XU, Zhun FAN. Survey on root cause analysis methods for complex systems based on causal discovery[J]. Systems Engineering and Electronics, 2025, 47(10): 3325-3352.

图/表 12

图1

图2

表1

现有基于约束的因果发现方法及其应用于复杂系统的优劣分析"

基于约束的方法	假设条件	应用于复杂系统的优点（特点）	应用于复杂系统的缺点
IC^[47]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设；④IID假设	①利用条件独立性检验确定骨架图；②依据V-结构特征及定向规则确定因果边方向	①观测数据一般难以满足所有假设条件；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；④无法准确捕捉时序数据间的因果关系；⑤对于高维变量的大规模观测数据而言，独立性或条件独立性检验需要较大计算开销，计算效率低
PC^[32,45]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设；④IID假设	①利用条件独立性检验确定骨架图；②依据V-结构特征及定向规则确定因果边方向	①观测数据一般难以满足所有假设条件；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；④无法准确捕捉时序数据间的因果关系；⑤对于高维变量的大规模观测数据而言，独立性或条件独立性检验需要较大计算开销，计算效率低
并行PC^[31]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设；④IID假设	相比于PC，并行计算能够显著提高算法的计算效率	①观测数据一般难以满足所有假设条件；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；④无法准确捕捉时序数据间的因果关系；⑤计算开销与PC相同
结合知识图谱技术的PC^[50]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设；④IID假设	①相比PC，结合了先验知识，使结果更准确；②具有更少的计算开销和更高的计算效率	①观测数据一般难以满足所有假设条件；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；④无法准确捕捉时序数据间的因果关系；⑤不具有泛化性
基于改进的条件独立性检验PC^[51]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设；④IID假设	因果发现准确率比PC有显著提高，与基于非线性回归的条件独立性检验相差不大，但计算效率显著提升	①观测数据一般难以满足所有假设条件；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；④无法准确捕捉时序数据间的因果关系
因果发现方法^[68]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设；④IID假设	①可处理混合数据（离散、连续数据）的因果发现；②结合PC-Stable和GES算法，同时设计新的条件独立性检验公式，提高算法效率和准确性；③输出结果与输入顺序无关	①观测数据一般难以满足所有假设条件；②无法区分马尔可夫等价类；③无法准确捕捉时序数据之间的因果关系
FCI^{[48,54−55,57]}	①因果马尔可夫假设；②因果忠诚性假设；③IID假设	观测变量不需要满足因果充分性假设，可以识别变量间的混杂因子	①计算复杂度高，且效率较低；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；④无法准确捕捉时序数据间的因果关系；⑤小样本性能差
真正快速因果推断（really fast causal inference，RFCI）^[58]	①因果马尔可夫假设；②因果忠诚性假设；③IID假设	相比于FCI，利用更少变量进行更少的条件独立性测试，计算复杂度较低，效率较高	①小样本性能差；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；④无法准确捕捉时序数据间的因果关系
贪婪快速因果推断（greedy fast causal inference，GFCI）^[59]	①因果马尔可夫假设；②因果忠诚性假设；③IID假设	①能够处理小样本数据；②因果发现的准确率高于RFCI	①计算效率低于RFCI；②输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差；③无法准确捕捉时序数据间的因果关系
因果循环推理（cyclic causal inference，CCI）^[60]	①因果马尔可夫假设；②因果忠诚性假设；③IID假设	①能够进行循环关系的因果发现，且优于循环因果发现算法；②计算效率高于Clingo答案集编程求解器	①需满足可以将循环因果过程表示为具有独立误差的线性结构方程模型的前提；②小样本性能差；③在非循环情况下，比FCI和RFCI的召回率低；④无法准确捕捉时序数据的因果关系
路径条件时间序列（path condition time series，PCTS）^[62]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	①观测变量不需要满足IID假设；②能够捕捉时序数据之间更准确的因果关系	①观测数据一般难以满足因果充分性假设；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差
结合霍克斯过程的PC^[64]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	①观测变量不需要满足IID假设；②能够捕捉时序数据之间更准确的因果关系	①观测数据一般难以满足因果充分性假设；②无法区分马尔可夫等价类；③输出结果取决于输入变量顺序，在高维变量环境下可能导致较大误差
PC-Stable^[67]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	①观测变量不需要满足IID假设；②相比于PC，其输出结果与输入变量顺序无关	①观测数据一般难以满足因果充分性假设；②无法区分马尔可夫等价类；③无法准确捕捉时序数据之间的因果关系
基于约束的非平稳/异构数据因果发现^[69]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	①能够基于异构观测数据有效识别具有非平稳局部因果机制的变量；②能根据数据分布变化所携带的信息确定因果方向；③能够捕捉时序数据之间更准确的因果关系	观测数据一般难以满足因果充分性假设

表1

图3

表2

表3

对基于评分的因果发现方法中现有搜索算法的对比分析"

搜索算法	假设条件	应用于复杂系统的优点（特点）	应用于复杂系统的缺点
K2算法^[90]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设；④假设变量有确定的先后顺序，需要指定变量最多的直接原因变量数量	使用贪心搜索选择评分最高的节点为父节点，以确定因果图	①难以确定变量的先后关系并指定最大父节点数量，适用性较差；②无法处理未观测混杂变量、样本选择偏差等问题
GES算法^[70]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	通过仅搜索相邻的因果图缩小搜索空间，提高搜索效率	①面对高维变量和大规模观测数据时，每搜索一步都要计算一次评分函数，耗时较长；②无法处理未观测混杂变量、样本选择偏差等问题
F-GES算法^[94]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	①对因果图进行分解并对缓存进行并行化，以快速从高维数据中推断因果关系；②对评分的更新通过缓存之前的分数得到，避免了重复计算；③引入了有限制的忠诚性假设	无法处理未观测混杂变量、样本选择偏差等问题
爬山算法^[76]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	在搜索过程中直接从临近的解空间（加边、减边、转边等，转边的前提是不会产生环）寻找最优解	①容易陷入局部最优，不一定能搜索到全局最优解；②无法处理未观测混杂变量、样本选择偏差等问题
进化算法^[91−92]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	可以利用相对较少的样本数量进行大范围搜索，不易陷入局部最优	①优化结果易受到例如群体大小等参数设置的影响；②无法处理未观测混杂变量、样本选择偏差等问题
粒子群优化算法^[98]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	可以利用相对较少的样本数量进行大范围搜索，不易陷入局部最优	①优化结果易受到例如群体大小等参数设置的影响；②无法处理未观测混杂变量、样本选择偏差等问题
蜂群算法^[99]	①因果马尔可夫假设；②因果忠诚性假设；③因果充分性假设	可以利用相对较少的样本数量进行大范围搜索，不易陷入局部最优	①优化结果易受到例如群体大小等参数设置的影响；②无法处理未观测混杂变量、样本选择偏差等问题

表3

图4

表4

现有基于函数因果模型的因果发现方法及其应用于复杂系统的优劣对比分析"

基于函数因果模型的方法	假设条件	应用于复杂系统的优点（特点）	应用于复杂系统的缺点
（ICA-）LiNGAM^[102,106]	①变量存在时间先后顺序；②变量的值是其原因变量的线性加和，外加一个噪声项和常数项；③因果充分性假设；④噪声项服从方差非零、均值为零的非高斯分布，且噪声之间相互独立	在先验知识缺乏的条件下，若观测数据满足假设，可以利用数据驱动的方法提升模型的因果发现能力	①观测变量难以满足所有假设条件；②利用ICA求解变量的因果顺序易陷入局部最优
Direct-LiNGAM^[110,107]	①变量存在时间先后顺序；②变量的值是其原因变量的线性加和，外加一个噪声项和常数项；③因果充分性假设；④噪声项服从方差非零、均值为零的非高斯分布，且噪声之间相互独立	①可以根据线性回归的残差与变量的独立性得到因果顺序，从而避免陷入局部最优的问题；②如果样本量无限，则能保证在少量固定步骤内收敛到正解；③可用于发现时序数据的因果关系	观测变量难以满足所有假设条件
ANM^[103]	①变量存在时间先后顺序；②因果充分性假设；③噪声项服从方差非零、均值为零的非高斯分布，且噪声之间相互独立	相比于LiNGAM，能够构建变量间更复杂的非线性关系模型	①相比于LiNGAM，参数组成更复杂，求解所需时间开销较大，对数据质量要求也较高；②对噪声干扰敏感，如果数据中存在噪声、缺失值、异常值，或者存在数据采样不均匀或不充分的情况，都有可能导致拟合结果的错误
MANM^[114]	①变量存在时间先后顺序；②噪声项服从方差非零、均值为零的非高斯分布，且噪声之间相互独立	相比于ICA-LiNGAM，在混合分布数据类型中具有更好的性能，在因果发现中具有更高的准确率	计算的时间复杂度较高
混杂级联非线性ANM^[115]	①变量存在时间先后顺序；②噪声项服从方差非零、均值为零的非高斯分布，且噪声之间相互独立	能够识别一对变量之间未测量的混杂因子和中间变量	无法处理全局因果结构搜索和等价类识别
两阶段因果结构学习算法^[116]	①变量存在时间先后顺序；②噪声项服从方差非零、均值为零的非高斯分布，且噪声之间相互独立	在真实因果结构数据集上的F1值平均提高了51%，显示出更高的准确性	应用于大规模变量时，需要通过大量计算确定因果边方向，计算复杂度高，开销大

表4

表5

现有基于格兰杰因果关系检验的因果发现方法及其应用于复杂系统的优劣对比分析"

基于格兰杰因果关系检验的方法	假设条件	应用于复杂系统的优点（特点）	应用于复杂系统的缺点
格兰杰因果关系检验方法^[116]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③已知滞后；④变量数据是平稳的；⑤采样频率与真正的因果滞后相匹配；⑥观测数据没有测量误差；⑦不存在无法观测的混杂因子	对于满足假设的观测数据，其预测结果较为准确	①观测数据一般难以满足所有假设条件；②无法准确预测非线性、不平稳的时序数据的格兰杰因果关系
①考虑所有可能的外生变量的方法^[130]；②将所有相关变量都当成内生变量的方法^{[113,131−132,137]}；③根据先验知识，事先排除错误因果关系的方法^[133−135]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③已知滞后；④变量数据是平稳的；⑤采样频率与真正的因果滞后相匹配；⑥观测数据没有测量误差	当存在无法观测的混杂因子时，通过考虑所有内生及外生变量的方式，也能够准确判断变量间的因果关系	①对于某些复杂系统，难以通过考虑所有相关变量的方式获得所有观测数据；②虽然不需要满足“不存在无法观测的混杂因子”的假设，实际上还是需要获取所有相关变量的观测数据
①基于MTD的格兰杰因果关系检验方法^[123]；②基于mLTD的格兰杰因果关系检验方法^[123]	①变量间的因果关系是线性的；②已知滞后；③变量数据是平稳的；④采样频率与真正的因果滞后相匹配；⑤观测数据没有测量误差；⑥不存在无法观测的混杂因子	①不需要满足变量数据均为连续值时间序列的假设；②解决了非凸目标和未知可识别性条件的两个问题	无法准确预测非线性、不平稳等特征的时序数据的格兰杰因果关系
①强格兰杰因果关系^[137]；②正则化的非参数估计程序^[138−139]；③网络格兰杰因果关系一致性估计^[140]	①变量数据均为连续值时间序列；②已知滞后；③变量数据是平稳的；④采样频率与真正的因果滞后相匹配；⑤观测数据没有测量误差；⑥不存在无法观测的混杂因子	不需要满足变量间的关系是线性的假设	仅限于加性相互作用机制
联合学习时间序列分类和格兰杰因果关系的方法^[141]	①变量数据均为连续值时间序列；②变量数据是平稳的；③采样频率与真正的因果滞后相匹配；④观测数据没有测量误差；⑤不存在无法观测的混杂因子	①不需要满足线性关系的假设；②不需要已知滞后期	滞后期是随机选择的，可能会面临滞后期过长或过短导致拟合不准确的情况
使用神经网络对非线性转换函数进行建模的格兰杰因果关系检验方法^[122]		①不需要满足线性关系的假设；②不需要已知滞后期；③在神经网络上部署稀疏性诱导惩罚，防止过拟合的同时保证拟合效果	基于神经网络的方法需要在训练时有大量数据支持
基于衰减假设的截断lasso惩罚的滞后期选择方法^[142]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③变量数据是平稳的；④采样频率与真正的因果滞后相匹配；⑤观测数据没有测量误差；⑥不存在无法观测的混杂因子	不需要事先指定滞后期	①不具有泛化性；②变量间的因果影响不一定是随时间衰减的
基于自适应阈值lasso惩罚的滞后期选择方法^[143]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③变量数据是平稳的；④采样频率与真正的因果滞后相匹配；⑤观测数据没有测量误差；⑥不存在无法观测的混杂因子	①不需要事先指定滞后期；②方法具有泛化性	计算复杂度较高，计算效率较低
基于衰减假设的分层的组lasso惩罚的滞后期选择方法^[144]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③变量数据是平稳的；④采样频率与真正的因果滞后相匹配；⑤观测数据没有测量误差；⑥不存在无法观测的混杂因子	①不需要事先指定滞后期；②该惩罚是凸函数，因此滞后估计的计算效率更高	变量间的因果影响不一定是随时间衰减的
①基于切换VAR模型的格兰杰因果关系检验方法^[145]；②处理非平稳性的替代方法^[121]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③采样频率与真正的因果滞后相匹配；④观测数据没有测量误差；⑤不存在无法观测的混杂因子	观测数据可以是非平稳的	无法准确预测非线性时序数据的格兰杰因果关系
处理非平稳性的替代方法^[146]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③采样频率与真正的因果滞后相匹配；④观测数据没有测量误差；⑤不存在无法观测的混杂因子	①观测数据可以是非平稳的；②不需要事先指定滞后期；③在高维环境下具有鲁棒性	无法准确预测非线性时序数据的格兰杰因果关系
基于混合高斯分布的格兰杰因果关系检验方法^[147]	①变量数据均为连续值时间序列；②变量间的因果关系是线性的；③已知滞后；④变量数据是平稳的；⑤观测数据没有测量误差；⑥不存在无法观测的混杂因子	仅基于观测到的子采样和混合频率数据就能对全套参数进行联合估计	无法准确预测具有非线性、不平稳等特征的时序数据的格兰杰因果关系

表5

表6

现有基于深度学习的因果发现方法及其应用于复杂系统的优劣对比分析"

基于深度学习的方法	数据特征		方法/模型	应用于复杂系统的优点（特点）	应用于复杂系统的缺点
面向IID数据的方法	一般数据	线性关系数据	NOTEARS^[155]	对于满足条件的观测数据，其预测结果较为准确	①对线性领域中非凸优化过程、非光滑评分函数或离散评分的应用困难；②无法准确预测非线性时序变量间的因果关系；③无法识别未观测的混杂因子的影响
	一般数据	非线性关系数据	基于GAE的因果结构学习方法^[156]，DAG-GNN^[157]，GraN-DAG^[158]，DAG-NoCurl^[159]	①可以较为准确地预测非线性时序变量间的因果关系；②可以进行离散变量的因果发现（DAG-GNN）；③计算效率较高，DAG-NoCurl尤其高于其他方法	①优化问题需要是非凸的；②无法识别未观测的混杂因子的影响
	干预数据	已知干预	ENCO^[164]	①即使在干预较少的变量和具有较小的样本量时，也表现稳健；②可以有效地恢复数百个节点组成的因果图	①未知干预变量时，难以有效分辨干预数据和非干预数据，可能做出错误判断；②无法识别未观测的混杂因子的影响
	干预数据	未知干预	SDI^[161]	能够基于观测数据，在未知干预中同时发现因果图和结构方程	①需要满足观测数据为离散值、干预稀疏、干预措施不叠加等假设；②无法识别未观测的混杂因子的影响
	存在未观测混杂因子影响的数据		CGNN^[167]， SAM^[168]，具有潜在变量的非线性因果发现^[169]， N-ADMG^[170]	能够有效识别未观测的混杂因子的影响	①计算成本较高（CGNN）；②需要满足相关的假设条件（具有潜在变量的非线性因果发现）
面向时间序列数据的方法	非线性关系数据		基于格兰杰因果关系检验的方法（economy-SRU^[174]，基于GVAR的方法^[176]，GrID-Net^[177]，CR-VAE^[176]）	能够有效提高时序变量间非线性格兰杰因果关系检验的准确性	需要满足数据平稳、因果充分性、采样频率与滞后相匹配等基本假设
	非线性关系数据		基于评分的方法（NTS-NOTEARS^[178]，Rhino^[179]，GANF^[180]）	①能够处理如非平稳、缓慢采样间隔的时间序列数据；②可以发现瞬时因果关系	评分函数的设置会直接影响因果发现结果的准确性
	多模态数据		InGRA^[181]，ACD^[182]	①能够提取多模态数据中的共性因果特征，生成因果图；②相比于针对不同数据分别提取因果图的方法，效率较高且能够避免过拟合问题	①需要处理的数据量大，对训练需要的数据规模、训练时间和资源消耗的要求较高；②在面对新的应用场景或不同分布的数据时，泛化能力可能不足
	干预数据		CRN^[183]	适用于动态系统中的因果发现问题	①需要进行随机干预和多次训练，可能会导致计算成本较高；②对于某些特定类型的因果关系，可能需要特定的干预策略才能有效学习
			IDYNO^[184]	适用于具有干预的动态数据	非参数化方法可能在高维数据中面临计算复杂度高和过拟合的风险
			LIN^[185]	①一种确定时序变量间因果关系的方法；②适用于处理潜在干预的非平稳数据	聚类方法可能对初始条件敏感，不同的初始化可能导致不同的聚类结果
	不规则采样数据		CUTS^[186]	能够解决时间序列数据的随机缺失或不均匀采样带来的问题	在数据缺失较多的情况下，进行数据插值可能会引入一定的误差
	不规则采样数据		SCOTCH^[187]	通过使用连续时间随机微分方程模拟数据的动态变化来处理不规则采样的时间序列数据	连续时间模型可能在实际应用中难以与离散时间数据直接对应，需要额外的离散化步骤以进行因果发现

表6

表7

现有影响强度计算方法及其应用于复杂系统的优劣对比分析"

分类	方法	方法描述	文献	应用于复杂系统的优点	应用于复杂系统的缺点
基于统计相关性的方法	皮尔逊相关系数	衡量两个连续且接近正态分布的变量之间线性关系强度和方向的指标	[29，31，50，62]	能够较为准确地衡量线性且独立的两个变量间的相关关系	①无法衡量非线性变量间的相关关系；②无法完全排除混杂因子的影响；③数据需要满足的条件较苛刻
	皮尔逊相关系数	衡量两个连续且接近正态分布的变量之间线性关系强度和方向的指标	[197]	①能够较为准确地衡量线性且独立的两个变量的相关关系；②当混杂因子可观测时，可以排除混杂因子的影响	无法衡量非线性变量间的相关关系
	斯皮尔曼等级相关系数	衡量两个变量之间的关系强度	—	①适用于定序变量或不满足正态分布假设的等间隔数据；②可以表征线性或非线性相关性关系	①无法完全排除混杂因子的影响；②计算开销较大；③渐近相对效率比皮尔逊相关系数低
	肯德尔等级相关系数	衡量两个变量之间的关系强度	—	①适用于定序变量或不满足正态分布假设的等间隔数据；②可以表征线性或非线性相关性关系	①无法完全排除混杂因子的影响；②计算开销较大；③渐近相对效率比皮尔逊相关系数低
基于回归系数计算的方法	函数因果模型	构建因果图中所有变量的回归模型，计算回归系数，即表示变量间的影响权重	[102，103，106−107，110，114−115]	当满足相应的假设条件时，能较为准确地判断变量间的时序因果影响权重	不同方法满足的假设条件不同（见表4）
基于回归系数计算的方法	格兰杰因果关系检验	构建因果图中所有变量的回归模型，计算回归系数，即表示变量间的影响权重	[113，121−124，130−147]	当满足相应的假设条件时，能较为准确地判断变量间的时序因果影响权重	①二元格兰杰因果关系检验方法无法排除混杂因子的影响；②不同方法满足的假设条件不同（见表5）
	式（5）	根据因果路径、利用观测数据计算两个变量之间的因果效应大小	[96]	能够基于因果图较为准确地计算变量间的因果影响大小	①相关函数的设计针对性较强，不具有泛化性；②当变量间关系复杂、变量数量较多时，变量间的因果路径较多，混杂因子数量也会增加，导致计算难度显著提升
基于因果效应计算的方法	有向传递函数	根据因果路径、利用观测数据计算两个变量之间的因果效应大小	[199]	能够基于因果图较为准确地计算变量间的因果影响大小	①相关函数的设计针对性较强，不具有泛化性；②当变量间关系复杂、变量数量较多时，变量间的因果路径较多，混杂因子数量也会增加，导致计算难度显著提升
	因果PACE	根据因果路径、利用观测数据计算路径的因果效应大小	[55]	能够针对不同的性能指标找到对应的关键因果路径	无法精确定位具体的根因
	因果路径贡献度	根据因果路径、利用观测数据计算路径的因果效应大小	[57]	对于可忽略因果影响权重，仅需考虑变量间因果路径数量和长度的系统而言，计算复杂度较低且效率较高	仅考虑变量间因果路径的数量和长度，没有考虑影响权重，在应用时需要谨慎评估其因果效应的准确性
基于节点评分的方法	PageRank 权重	基于因果图对变量的贡献度进行评分，以计算对其它变量或异常变量的影响大小	[201]	直接对因果图中各节点对于全局变量或异常变量的贡献大小进行单独打分，在此基础上进行根因识别时，不需要考虑因果路径的影响强度大小	评分方法的设计较为主观，一般仅针对固定的应用场景
	振荡显著性指数	基于因果图对变量的贡献度进行评分，以计算对其它变量或异常变量的影响大小	[134]	直接对因果图中各节点对于全局变量或异常变量的贡献大小进行单独打分，在此基础上进行根因识别时，不需要考虑因果路径的影响强度大小	评分方法的设计较为主观，一般仅针对固定的应用场景
	CUSUM 评分	基于因果图对变量的贡献度进行评分，以计算对其它变量或异常变量的影响大小	[32]	直接对因果图中各节点对于全局变量或异常变量的贡献大小进行单独打分，在此基础上进行根因识别时，不需要考虑因果路径的影响强度大小	评分方法的设计较为主观，一般仅针对固定的应用场景
	RS	基于因果图对变量的贡献度进行评分，以计算对其它变量或异常变量的影响大小	[95]	直接对因果图中各节点对于全局变量或异常变量的贡献大小进行单独打分，在此基础上进行根因识别时，不需要考虑因果路径的影响强度大小	评分方法的设计较为主观，一般仅针对固定的应用场景
	IERE	基于因果图对变量的贡献度进行评分，以计算对其它变量或异常变量的影响大小	[64]	直接对因果图中各节点对于全局变量或异常变量的贡献大小进行单独打分，在此基础上进行根因识别时，不需要考虑因果路径的影响强度大小	评分方法的设计较为主观，一般仅针对固定的应用场景

表7

表8

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分类及描述	评分方法	应用于复杂系统的优点（特点）	应用于复杂系统的缺点
贝叶斯评分函数：结合先验信息的评分函数，即利用先验知识和数据寻求后验概率最大的网络结构	K2^[75]	—	①需要指定变量先后顺序以及最大父节点数量；②容易陷入局部最优
	K2+节点排序方法^[77−78]	—	仅针对特定场景对节点进行排序，不具有泛化性
	BDe^[76]	不需要指定变量的先后顺序和最大父节点数量	①观测数据需要含有各种状态或涵盖各个变量；②先验概率服从狄利克雷分布；③无法区分马尔可夫等价类
	BDeu^[76]	不需要指定变量的先后顺序和最大父节点数量	①观测数据需要含有各种状态或涵盖各个变量；②先验概率服从狄利克雷分布；③无法区分马尔可夫等价类
信息论评分函数：利用编码理论和信息论中的MDL原理找到使网络描述长度和样本编码长度之和最小的图模型	MDL^[80]	不依赖先验信息	观测数据量较小时，容易欠拟合；观测数据量较大时，容易过拟合
	AIC^[81]	①限制参数个数；②对似然函数进行了惩罚，以提高准确性	①对样本个数没有相应惩罚，可能导致模型精度过高造成过拟合；②无法区分马尔可夫等价类
	BIC^[82]	①限制参数个数；②除似然函数，还考虑对样本个数的惩罚，有效防止过拟合	无法区分马尔可夫等价类
	MIT^[84,88]	①基于条件独立性检验的互信息和卡方分布构造评分函数；②用网络的局部结构复杂度作为惩罚项，计算复杂度较低	①极易过高估计变量之间的相互作用关系，导致错误判断假阳性边；②无法区分马尔可夫等价类
	CVMIC^[68]	能够对基于混合类型的高维数据的因果图进行评分	无法区分马尔可夫等价类

数据类型	云服务系统	计算机专用网络	工业生产系统	生物/医学系统	社会科学系统	城市系统	机器人系统	气候系统	经济系统
指标数据	[2，29−32，50，54，62，68，95，110−111，202]	[206]	[28，33，79，112−113，133，136，199，203]	[60，69，76−77， 91−92，98−99， 140，161，164]	[96，106−107]	[51，161，164]	[55，77−78]	[77，114，147]	[146]
拓扑连接数据	[31]	[64]	[79，133， 135，199]	—	—	—	—	—	—
日志数据	—	[64，67，108]	[57，75， 134−135]	[122，132，138− 140，142−143， 155，157−159， 167，169]	—	—	[141]	—	[130，132，144−145，147]

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基于因果发现的复杂系统根因分析方法综述

Survey on root cause analysis methods for complex systems based on causal discovery

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