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

Abstract

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

CLC Number:

TP 182

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.

Figures/Tables 12

Fig.1

Fig.2

Table 1

Analysis of existing constraint-based causal discovery methods and their advantages and disadvantages in complex systems"

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

Table 1

Fig.3

Table 2

Table 3

Comparative analysis of existing search algorithms used in score-based causal discovery methods"

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

Table 3

Fig.4

Table 4

Comparative analysis of existing causal discovery methods based on functional causal models and their advantages and disadvantages applied to complex systems"

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

Table 4

Table 5

Comparative analysis of existing causal discovery methods based on Granger causality test and their advantages and disadvantages applied to complex systems"

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

Table 5

Table 6

Comparative analysis of existing causal discovery methods based on deep learning and their advantages and disadvantages applied to complex systems"

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

Table 6

Table 7

Comparative analysis of existing influence strength calculation methods and their advantages and disadvantages analysis applied to complex systems"

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

Table 7

Table 8

References 226

1	SOLDANI J, BROGI A. Anomaly detection and failure root cause analysis in （micro）service-based cloud applications: a survey[J]. ACM Computing Surveys, 2022, 55 (3): 59.
2	MA M, LIN W L, PAN D S, et al. Self-adaptive root cause diagnosis for large-scale microservice architecture[J]. IEEE Trans. on Services Computing, 2020, 15 (3): 1399- 1410.
3	LI S Y, MA S Y, CUI L Y, et al. Overview of root cause localization method in microservice architecture[J]. Frontiers of Data & Computing, 2022, 4 (3): 78- 89.
4	MAHTO D, KUMAR A. Root cause analysis for optimizing manufacturing processes: a case study on automotive component production[J]. International Journal of Production Research, 2010, 48 (15): 4523- 4540.
5	CHIANG L H, JIANG B B, ZHU X X, et al. Diagnosis of multiple and unknown faults using the causal map and multivariate statistics[J]. Journal of Process Control, 2015, 28, 27- 39. doi: 10.1016/j.jprocont.2015.02.004
6	NAGHAVI-KONJIN Z, MORTAZAVI S B, ASILIAN-MAHABADI H, et al. Ranking the occupational incident contributory factors: a Bayesian network model for the petroleum industry[J]. Process Safety and Environmental Protection, 2020, 137, 352- 357. doi: 10.1016/j.psep.2020.01.038
7	BABAOGLU O, JELASITY M, ALBERTO M, et al. Self-star properties in complex information systems: conceptual and practical foundations[M]. Heidelberg: Springer, 2005.
8	BU F B, JIN G. Military system evaluation method based on complexity theory[C]//Proc. of the 3rd Academic Conference on Systems Engineering, 2021: 188−193.
9	孔祥玉, 王晓兵, 李红增, 等. 面向工业平稳/非平稳复杂系统的在线故障监测技术[J]. 浙江大学学报（工学版）, 2021, 55 (10): 1856- 1866. doi: 10.3785/j.issn.1008-973X.2021.10.007
	KONG X Y, WANG X B, LI H Z, et al. On-line fault monitoring technology for industrial stationary/nonstationary complex system[J]. Journal of Zhejiang University: Engineering Science, 2021, 55 (10): 1856- 1866. doi: 10.3785/j.issn.1008-973X.2021.10.007
10	王博, 华庆一, 舒新峰. 基于云平台日志的故障检测和复杂构件系统即时可靠性度量研究[J]. 计算机科学, 2022, 49 (12): 125- 135. doi: 10.11896/jsjkx.220200106
	WANG B, HUA Q Y, SHU X F. Study on anomaly detection and real-time reliability evaluation of complex component system based on log of cloud platform[J]. Computer Science, 2022, 49 (12): 125- 135. doi: 10.11896/jsjkx.220200106
11	SHANG D, SHANG P J. The dependence index based on martingale difference correlation: an efficient tool to distinguish different complex systems[J]. Expert Systems with Applications, 2022, 213, 119- 284.
12	LI X H, WANG J, TAN J H, et al. A graph neural network-based stock forecasting method utilizing multi-source heterogeneous data fusion[J]. Multimedia Tools and Applications, 2022, 81 (30): 43753- 43775. doi: 10.1007/s11042-022-13231-1
13	李军亮, 祝华远, 王利明, 等. 考虑混合维修策略的复杂系统区间可用度[J]. 系统工程与电子技术, 2020, 42 (5): 1190- 1196. doi: 10.3969/j.issn.1001-506X.2020.05.29
	LI J L, ZHU H Y, WANG L M, et al. Interval availability for complex system based on mixed maintenance strategy[J]. Systems Engineering and Electronics, 2020, 42 (5): 1190- 1196. doi: 10.3969/j.issn.1001-506X.2020.05.29
14	胡涛, 马晨辉, 周晓柳婷, 等. 航天复杂系统的加权模糊Petri网故障诊断建模[J]. 计算机集成制造系统, 2019, 25 (10): 2580- 2586.
	HU T, MA C H, ZHOU X L T, et al. Fault diagnosis method for complex aerospace systems based on weighted fuzzy Petri net[J]. Computer Integrated Manufacturing Systems, 2019, 25 (10): 2580- 2586.
15	李果. 基于循环神经网络的复杂系统状况评估技术研究[D]. 北京: 北京邮电大学, 2022.
	LI G. Research on the condition evaluation technology of the complex system based on recurrent neural network[D]. Beijing: Beijing University of Posts and Telecommunications, 2022.
16	CHO Y S, KIM S B. Quality-discriminative localization of multi-sensor signals for root cause analysis[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2021, 52 (7): 4374- 4387.
17	OLIVEIRA E, MIGUEIS V L, BORGES J L. Automatic root cause analysis in manufacturing: an overview & conceptualization[J]. Journal of Intelligent Manufacturing, 2023, 34 (5): 2061- 2078. doi: 10.1007/s10845-022-01914-3
18	刘一萌, 白铭阳, 张小可, 等. 复杂系统可靠性[J]. 山东科学, 2024, 37 (2): 74- 84. doi: 10.3976/j.issn.1002-4026.20240025
	LIU Y M, BAI M Y, ZHANG X K, et al. Complex system reliability[J]. Shandong Science, 2024, 37 (2): 74- 84. doi: 10.3976/j.issn.1002-4026.20240025
19	杨桄, 李文强, 万昌富. 面向核心问题的系统原因识别方法与创新设计研究[J]. 中国机械工程, 2022, 33 (15): 1810- 1820. doi: 10.3969/j.issn.1004-132X.2022.15.007
	YANG G, LI W Q, WAN C F. Core-problem oriented system cause identification method and innovative design research[J]. China Mechanical Engineering, 2022, 33 (15): 1810- 1820. doi: 10.3969/j.issn.1004-132X.2022.15.007
20	ABUBAKAR A, ZADEH P B, JANICKE H, et al. Root cause analysis (RCA) as a preliminary tool into the investigation of identity theft[C]//Proc. of the International Conference on Cyber Security and Protection of Digital Services, 2016.
21	OLIVEIRA E, MIGUEIS V L, BORGES J L. Data-driven root cause analysis in smart manufacturing: a systematic review and framework[J]. Journal of Manufacturing Systems, 2024, 68, 512- 530.
22	PERCARPIO K B, WATTS B V, WEEKS W B. The effectiveness of root cause analysis: what does the literature tell us?[J]. The Joint Commission Journal on Quality and Patient Safety, 2008, 34 (7): 391- 398. doi: 10.1016/S1553-7250(08)34049-5
23	DUAN P, HE Z Z, HE Y H, et al. Root cause analysis approach based on reverse cascading decomposition in QFD and fuzzy weight ARM for quality accidents[J]. Computers & Industrial Engineering, 2020, 147, 106643.
24	ITO A, HAGSTROM M, BOKRANTZ J, et al. Improved root cause analysis supporting resilient production systems[J]. Journal of Manufacturing Systems, 2022, 64, 468- 478.
25	PEARL J. Models, reasoning and inference [M]. Cambridge: Cambridge University Press, 2000.
26	蔡瑞初, 陈薇, 张坤, 等. 基于非时序观察数据的因果关系发现综述[J]. 计算机学报, 2017, 40 (6): 1470- 1490. doi: 10.11897/SP.J.1016.2017.01470
	CAI R C, CHEN W, ZHANG K, et al. Review of causality findings based on nontemporal observation data[J]. Journal of Computer Science, 2017, 40 (6): 1470- 1490. doi: 10.11897/SP.J.1016.2017.01470
27	RICHENS J G, LEE C M, JOHRI S. Publisher correction: improving the accuracy of medical diagnosis with causal machine learning[J]. Nature Communications, 2020, 11 (1): 4754. doi: 10.1038/s41467-020-18310-1
28	MORI J, MAHALEC’ V, YU J. Identification of probabilistic graphical network model for root-cause diagnosis in industrial processes[J]. Computers & Chemical Engineering, 2014, 71, 171- 209.
29	WANG P, XU J M, MA M, et al. CloudRanger: root cause identification for cloud native systems[C]//Proc. of the 18th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing, 2018: 492−502.
30	MA M, LIN W L, PAN D S, et al. ServiceRank: root cause identification of anomaly in large-scale microservice architectures[J]. IEEE Trans. on Dependable and Secure Computing, 2021, 19 (5): 3087- 3100.
31	LIN J J, CHEN P F, ZHENG Z B. Microscope: pinpoint performance issues with causal graphs in micro-service environments[C]//Proc. of the 16th International Conference on Service Oriented Computing, 2018: 3−20.
32	CHEN P F, QI Y, HOU D. CauseInfer: automated end-to-end performance diagnosis with hierarchical causality graph in cloud environment[J]. IEEE Trans. on Services Computing, 2016, 12 (2): 214- 230.
33	UCHIDA Y, FUJIWARA K, SAITO T, et al. Causal plot: causal-based fault diagnosis method based on causal analysis[J]. Processes, 2022, 10 (11): 2269. doi: 10.3390/pr10112269
34	QIU H D, LIU Y, SUBRAHMANYA N A, et al. Granger causality for time-series anomaly detection[C]//Proc. of the IEEE 12th International Conference on Data Mining, 2012: 1074−1079.
35	CHENG L, GUO R C, MORAFFAH R, et al. Evaluation methods and measures for causal learning algorithms[J]. IEEE Trans. on Artificial Intelligence, 2022, 3 (6): 924- 943. doi: 10.1109/TAI.2022.3150264
36	YAO L Y, CHU Z X, LI S, et al. A survey on causal inference[J]. ACM Transaction on Knowledge Discovery from Data, 2021, 15 (5): 1- 46.
37	HECKMAN J J. Microdata, heterogeneity, and the evaluation of public policy: Nobel lecture[J]. Journal of Political Economy, 2001, 109 (4): 673- 748. doi: 10.1086/322086
38	HECKMAN J J. Building bridges between structural and program evaluation approaches to evaluating policy[J]. Journal of Economic Literature, 2010, 48 (2): 356- 398. doi: 10.1257/jel.48.2.356
39	李家宁, 熊睿彬, 兰艳艳. 因果机器学习的前沿进展综述[J]. 计算机研究与发展, 2023, 60 (1): 59- 84. doi: 10.7544/issn1000-1239.202110780
	LI J N, XIONG R B, LAN Y Y. Review of the frontier advances in causal machine learning[J]. Computer Research and Development, 2023, 60 (1): 59- 84. doi: 10.7544/issn1000-1239.202110780
40	MIAO W, LIU C C, GENG Z. Statistical methods for causal inference[J]. SCIENCE CHINA Mathematics, 2018, 48 (12): 1753- 1778.
41	VUKOVIC M, THALMANN S. Causal discovery in manufacturing: a structured literature review[J]. Journal of Manufacturing and Materials Processing, 2022, 6 (1): 10. doi: 10.3390/jmmp6010010
42	SOLE M, MUNTES-MULERO V, RANA A I, et al. Survey on models and techniques for root-cause analysis[EB/OL]. [2024-05-28]. https://arxiv.org/abs/1701.08546.
43	MA Q, LI H, THORSTENSON A. A big data-driven root cause analysis system: application of machine learning in quality problem solving[J]. Computers & Industrial Engineering, 2021, (160): 107580.
44	KAO E K. Causal inference under network interference: a framework for experiments on social networks[D]. Cambridge: Harvard University, 2017.
45	SPIRTES P, GLYMOUR C, SCHEINES R, et al. Causation, prediction, and search[M]. Massachusetts: MIT Press, 2000.
46	GONG C, YAO D, ZHANG C Z, et al. Causal discovery from temporal data: an overview and new perspectives[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2303.10112.
47	VERMA T, PEARL J. Equivalence and synthesis of causal models[C]//Proc. of the 6th Annual Conference on Uncertainty in Artificial Intelligence, 1990: 255−270.
48	SPIRTES P L, MEEK C, RICHARDSON T. Causal inference in the presence of latent variables and selection bias[EB/OL]. [2024-05-28]. https://arxiv.org/abs/1302.4983.
49	SPIRTES P L, ZHANG K. Causal discovery and inference: concepts and recent methodological advances[J]. Applied Informations, 2016, 3 (1): 1- 28. doi: 10.1186/s40535-016-0018-x
50	QIU J, DU Q F, YIN K L, et al. A causality mining and knowledge graph-based method of root cause diagnosis for performance anomaly in cloud applications[J]. Applied Sciences, 2020, 10 (6): 2166. doi: 10.3390/app10062166
51	陈少凡, 韦程东, 何国源, 等. 基于混合条件独立性测试的因果发现算法[J]. 南宁师范大学学报（自然科学版）, 2023, 40 (2): 50- 60.
	CHEN S F, WEI C D, HE G Y, et al. Causal discovery algorithm based on mixed condition independence testing[J]. Journal of Nanning Normal University （Natural Science Edition）, 2023, 40 (2): 50- 60.
52	ZHANG J J. Causal inference and reasoning in causally insufficient systems[D]. Berkeley: University of California, 2006.
53	RICHARDSON T, SPIRTES P. Ancestral graph Markov models[J]. The Annals of Statistics, 2002, 30 (4): 962- 1030.
54	CHEN Y J, YANG X, LIN Q W, et al. Outage prediction and diagnosis for cloud service systems[C]//Proc. of the World Wide Web Conference, 2019: 2659−2665.
55	HOSSEN M A, KHARADE S, SCHMERL B, et al. CaRE: finding root causes of configuration issues in highly-configurable robots[J]. IEEE Robotics and Automation Letters, 2023, 8 (7): 4115- 4122. doi: 10.1109/LRA.2023.3280810
56	KOCAOGLU M, SHAKKOTTAI S, DIMAKIES A G. Applications of common entropy for causal inference[J]. Advances in Neural Information Processing Systems, 2020, 33, 17514- 17525.
57	WU J P, LU Y J, LI D Z, et al. Key influencing factors identification in complex systems based on heuristic causal inference[J]. Applied Sciences, 2023, 13 (19): 10575. doi: 10.3390/app131910575
58	COLOMBO D, MAATHUIS M H, KALISCH M, et al. Learning high-dimensional directed acyclic graphs with latent and selection variables[J]. The Annals of Statistics, 2012, 40 (1): 294- 321.
59	OGARRIO J M, SPIRTES P L, RAMSEY J. A hybrid causal search algorithm for latent variable models[C]//Proc. of the Conference on Probabilistic Graphical Models, 2016: 368−379.
60	STROBL E V. A constraint-based algorithm for causal discovery with cycles, latent variables and selection bias[J]. International Journal of Data Science and Analytics, 2019, 8 (1): 33- 56. doi: 10.1007/s41060-018-0158-2
61	FLAXMAN S R, NEILL D B, SMOLA A J. Gaussian processes for independence tests with non-IID data in causal inference[J]. ACM Transactions on Intelligent Systems and Technology, 2015, 7 (2): 22.
62	MENG Y, ZHANG S L, SUN Y Q, et al. Localizing failure root causes in a microservice through causality inference[C]//Proc. of the IEEE/ACM 28th International Symposium on Quality of Service, 2020.
63	RUNGE J, NOWACK P, KRETSCHMER M, et al. Detecting and quantifying causal associations in large nonlinear time series datasets[J]. Science Advances, 2019, 5 (11): 4996. doi: 10.1126/sciadv.aau4996
64	ZHANG K L, KALANDER M, ZHOU M, et al. An influence-based approach for root cause alarm discovery in telecom networks [C]//Proc. of the Service-Oriented Computing Workshops: AIOps, CFTIC, STRAPS, AI-PA, AI-IOTS, and Satellite Events, 2021: 124−136.
65	HAWKES A G. Spectra of some self-exciting and mutually exciting point processes[J]. Biometrika, 1971, 58 (1): 83- 90. doi: 10.1093/biomet/58.1.83
66	COLOMBO D, MAATHUIS M. Order independent constraint-based causal structure learning[J]. Journal Of Machine Learning Research, 2014, 15 (1): 3741- 3782.
67	KOBAYASHI S, OTOMO K, FUKUDA K, et al. Mining causality of network events in log data[J]. IEEE Trans. on Network and Service Management, 2017, 15 (1): 53- 67.
68	LI Y, XIA R, LIU C C, et al. A Hybrid causal structure learning algorithm for mixed-type data[C]// /Proc. of the AAAI Conference on Artificial Intelligence, 2022.
69	ZHANG K, HUANG B W, ZHANG J J, et al. Causal discovery from nonstationary/heterogeneous data: skeleton estimation and orientation determination[C]//Proc. of the 26th International Joint Conference on Artificial Intelligence, 2017: 1347−1353.
70	CHICKERING D M. Optimal structure identification with greedy search[J]. Journal of Machine Learning Research, 2002, 3(3): 48.
71	KOLLER D, FRIEDMAN N. Probabilistic graphical models: principles and techniques [M]. Massachusetts: MIT press, 2009.
72	BOLLEN K A. Structural equations with latent variables[M]. New York: John Wiley & Sons, 1989.
73	FISHER D H, LENZ H J. Learning from data: artificial intelligence and statistics V[M]. Berlin, Germany: Springer Science & Business Media, 1996.
74	朱明敏. 贝叶斯网络结构学习与推理研究[D]. 西安: 西安电子科技大学, 2013.
	ZHU M M. Research on Bayesian network structure learning and inference[D]. Xi’an: Xdian University, 2013.
75	WANG J, LI H G, HUANG J W, et al. A data similarity-based analysis to consequential alarms of industrial processes[J]. Journal of Loss Prevention in the Process Industries, 2015, 35, 29- 34. doi: 10.1016/j.jlp.2015.03.005
76	HECKERMAN D, GEIGER D, CHICKERING D M. Learning Bayesian networks: the combination of knowledge and statistical data[J]. Machine Learning, 1995, 20 (3): 197- 243. doi: 10.1023/A:1022623210503
77	CHEN X W, ANANTHA G, LIN X T. Improving Bayesian network structure learning with mutual information-based node ordering in the K2 algorithm[J]. IEEE Trans. on Knowledge and Data Engineering, 2008, 20 (5): 628- 640. doi: 10.1109/TKDE.2007.190732
78	SONG K, KIM D W. An efficient node ordering method using the conditional frequency for the K2 algorithm[J]. Pattern Recognition Letters, 2014, 40 (4): 80- 87.
79	DI G J, GERONIMO G, ALBAI D B, et al. Integrating process data and plant topology for fault propagation analysis in chemical industries[J]. Chemical Engineering Research and Design, 2013, 91 (8): 1567- 1578.
80	RISSANEN J. Modeling by shortest data description[J]. Automatica, 1978, 14 (5): 465- 471. doi: 10.1016/0005-1098(78)90005-5
81	AKAIKE H. Information theory and an extension of the maximum likelihood principle[J]. IEEE Trans. On Automatic Control, 1974, 19 (6): 716- 723. doi: 10.1109/TAC.1974.1100705
82	NEATH A A, CAVANAUGH J E. The Bayesian information criterion: background, derivation, and applications[J]. Wiley Interdisciplinary Reviews: Computational Statistics, 2012, 4 (2): 199- 203. doi: 10.1002/wics.199
83	SCHWARZ G. Estimating the dimension of a model[J]. Automatica, 1978, 6 (2): 461- 464.
84	CAMPOS L M. A scoring function for learning Bayesian networks based on mutual information and conditional independence tests[J]. Journal of Machine Learning Research, 2006, 7 (2): 2149- 2187.
85	GALBRUN E. The minimum description length principle for pattern mining: a survey[J]. Data Mining and Knowledge Discovery, 2022, 36 (5): 1679- 1727. doi: 10.1007/s10618-022-00846-z
86	BURNHAM K P, ANDERSON D R. Multi-model inference: understanding AIC and BIC in model selection[J]. International Journal of Wildland Fire, 2012, 21 (2): 261- 304.
87	CAPISTRANO A J S, SEIDEL P T Z, DUARTE H R. Sub-horizon linear Nash-Greene perturbations with constraints on H（z） and the deceleration parameter q（z）[J]. Physics of the Dark Universe, 2020, 31, 100760.
88	刘飞, 张绍武, 高红艳. 基于部分互信息和贝叶斯打分函数的基因调控网络构建算法[J]. 西北工业大学学报, 2017, 35 (5): 876- 883. doi: 10.3969/j.issn.1000-2758.2017.05.020
	LIU F, ZHANG S W, GAO H Y. Algorithm for constructing gene regulatory networks based on partial mutual information and Bayesian scoring functions[J]. Journal of Northwestern Polytechnical University, 2017, 35 (5): 876- 883. doi: 10.3969/j.issn.1000-2758.2017.05.020
89	ZHAO J X, ZHOU Y, ZHANG X, et al. Part mutual information for quantifying direct associations in networks[J]. Proceedings of the National Academy of Sciences, 2016, 113 (18): 5130- 5135. doi: 10.1073/pnas.1522586113
90	COOPER G F, HERSKOVITS E. A Bayesian method for the induction of probabilistic networks from data[J]. Machine Learning, 1992, 9 (4): 309- 347. doi: 10.1023/A:1022649401552
91	郭文强, 毛玲玲, 黄梓轩, 等. 改进进化算法的贝叶斯网络结构学习及其应用[J]. 河南科技大学学报（自然科学版）, 2022, 43 (2): 34- 40.
	GUO W Q, MAO L L, HUANG Z X, et al. Bayesian network structure learning with improved evolutionary algorithms and its applications[J]. Journal of Henan University of Science & Technology, 2022, 43 (2): 34- 40.
92	武梦娇, 刘继. 基于微生物遗传算法的贝叶斯网络结构学习[J]. 重庆科技学院学报（自然科学版）, 2020, 22 (6): 70- 74.
	WU M J, LIU J. Bayesian network structure learning based on microbial genetic algorithm[J]. Journal of Chongqing University of Science and Technology （Natural Sciences Edition）, 2020, 22 (6): 70- 74.
93	SMITH S M, MILLER K L, SALIMI-KHORSHIDI G, et al. Network modelling methods for FMRI[J]. Neuroimage, 2011, 54 (2): 875- 891. doi: 10.1016/j.neuroimage.2010.08.063
94	RAMSEY J, GLYMOUR M, SANCHEZ-ROMERO R, et al. A million variables and more: the fast greedy equivalence search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images[J]. International Journal of Data Science and Analytics, 2017, 3 (2): 121- 129. doi: 10.1007/s41060-016-0032-z
95	YANG W Z, ZHANG K, HOI S T H. A Causal approach to detecting multivariate time-series anomalies and root causes [EB/OL]. [2024-05-28]. https://arxiv.org/abs/2206.15033.
96	XIE X, DU F, WU Y C. A visual analytics approach for exploratory causal analysis: exploration, validation, and applications[J]. IEEE Trans. on Visualization and Computer Graphics, 2020, 27 (2): 1448- 1458.
97	刘浩然, 王念太, 王毅, 等. 基于V-结构&对数似然函数定向与禁忌爬山的贝叶斯网络结构算法[J]. 电子与信息学报, 2021, 43 (11): 3272- 3281. doi: 10.11999/JEIT210032
	LIU H R, WANG N T, WANG Y, et al. Bayesian network structure algorithm based on V-structure & log-likelihood orientation and tabu hill climbing[J]. Journal of Electronics & Information Technology, 2021, 43 (11): 3272- 3281. doi: 10.11999/JEIT210032
98	董文佳, 方洋旺, 彭维仕, 等. 基于MMPC-FPSO贝叶斯网络混合结构学习方法[J]. 空军工程大学学报, 2024, 25 (2): 76- 84. doi: 10.3969/j.issn.2097-1915.2024.02.009
	DONG W J, FANG Y W, PENG S W, et al. A hybrid structure learning method based on MMPC-FPSO for Bayesian networks[J]. Journal of Air Force Engineering University, 2024, 25 (2): 76- 84. doi: 10.3969/j.issn.2097-1915.2024.02.009
99	汪春峰, 蒋妍. 基于蜂群算法和遗传算法的贝叶斯网络结构混合学习方法[J]. 河南师范大学学报（自然科学版）, 2015, 43 (4): 16- 20.
	WANG C F, JIANG Y. A hybrid algorithm for learning Bayesian Network structure based on artificial bee colony and genetic algorithm[J]. Journal of Henan Normal University （Natural Science Edition）, 2015, 43 (4): 16- 20.
100	QIAO J, CAI R C, ZHANG K, et al. Causal discovery with confounding cascade nonlinear additive noise models[J]. ACM Transaction on Intelligent Systems and Technology, 2021, 12 (6): 1- 28.
101	ZHANG K, WANG Z K, ZHANG J J, et al. On estimation of functional causal models: general results and application to the post-nonlinear causal model[J]. ACM Transaction on Intelligent Systems and Technology, 2015, 7 (2): 1- 22.
102	SHIMIZU S, HOYER P O, HYVARINEN A, et al. A linear non-Gaussian acyclic model for causal discovery[J]. Journal of Machine Learning Research, 2006, 7 (4): 2003- 2030.
103	PETERS J, MOOIJ J M, JANZING D, et al. Causal discovery with continuous additive noise models[J]. Journal of Machine Learning Research, 2014, 15 (1): 2009- 2053.
104	HYVARINEN A, OJA E. Independent component analysis: algorithms and applications[J]. Neural Networks, 2000, 13 (4/5): 411- 430.
105	LOPEZ-PAZ D, MUANDET K, SCHOLKOPF B, et al. Towards a learning theory of cause-effect inference[C]//Proc. of the International Conference on Machine Learning, 2015: 1452−1461.
106	CHEN J Y, KIBRIYA S, BESSLER D, et al. The relationship between conflict events and commodity prices in Sudan[J]. Journal of Policy Modeling, 2018, 40 (4): 663- 684. doi: 10.1016/j.jpolmod.2018.01.014
107	SHIMIZU S, INAZUMI T, SOGAWA Y, et al. DirectLiNGAM: a direct method for learning a linear non-Gaussian structural equation model[J]. Journal of Machine Learning Research, 2011, 12 (2): 1225- 1248.
108	WINCHESTER G, PARISIS G, BERTHOUZE L. Exploiting functional connectivity inference for efficient root cause analysis[C]//Proc. of the IEEE/IFIP Network Operations and Management Symposium, 2022.
109	MESSAGER A, PARISIS G, KISS I Z, et al. Inferring functional connectivity from time-series of events in large scale network deployments[J]. IEEE Trans. on Network and Service Management, 2019, 16 (3): 857- 870. doi: 10.1109/TNSM.2019.2932896
110	WU L, TORDSSON J, BOGATINOVSKI J. MicroDiag: fine-grained performance diagnosis for microservice systems[C]//Proc. of the IEEE/ACM International Workshop on Cloud Intelligence, 2021: 31−36.
111	XIN R Y, LIU H Y, CHEN P, et al. FIRED: a fine-grained robust performance diagnosis framework for cloud applications[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2209.01970.
112	HAN Y H, LI Q, WANG C, et al. A novel knowledge enhanced graph neural networks for fault diagnosis with application to blast furnace process safety[J]. Process Safety and Environmental Protection, 2022, 166, 143- 157. doi: 10.1016/j.psep.2022.08.014
113	WANG S, ZHAO Q, HAN Y H, et al. Root cause diagnosis for process faults based on multi-sensor time-series causality discovery[J]. Journal of Process Control, 2023, 122, 27- 40. doi: 10.1016/j.jprocont.2022.12.006
114	PARIDA P K, MARWALA T, CHAKRAVERTY S. A multivariate additive noise model for complete causal discovery[J]. Neural Networks, 2018, 10, 44- 54.
115	QIAO J, CAI R C, HAO Z F. Causal structure learning algorithm based on cascade additive noise model[J]. Computer Engineering, 2022, 48 (1): 93- 98.
116	GRANGER C W J. Investigating causal relations by econometric models and cross-spectral methods[J]. Econometrica: Journal of the Econometric Society, 1969, 37 (3): 424- 438. doi: 10.2307/1912791
117	SHOJAIE A, FOX E B. Granger causality: a review and recent advances[J]. Annual Review of Statistics and its Application, 2022, 9 (1): 289- 319. doi: 10.1146/annurev-statistics-040120-010930
118	蔡瑞初, 郝志峰. 大数据中的因果关系发现[M]. 北京: 科学出版社, 2018.
	CAI R C, HAO Z F. Causal discovery in big data[M]. Beijing: Science Press, 2018.
119	SETH AK, BARRETT AB, BARNETT L. Granger causality analysis in neuroscience and neuroimaging[J]. Neuroscience, 2015, 35 (8): 3293- 3297. doi: 10.1523/JNEUROSCI.4399-14.2015
120	KONTOYIANNIS I, SKOULARIDOU M. Estimating the directed information and testing for causality[J]. IEEE Trans. on Information, 2016, 62 (11): 6053- 6067. doi: 10.1109/TIT.2016.2604842
121	SAFIKHANI A, SHOJAIE A. Joint structural break detection and parameter estimation in high-dimensional nonstationary VAR models[J]. American Statistical Association, 2022, 117 (537): 251- 264. doi: 10.1080/01621459.2020.1770097
122	TANK A, COVERT I, FOTI N, et al. Neural Granger causality[J]. IEEE Trans. on Pattern Analysis and Machine Intelligence, 2022, 44 (8): 4267- 4279.
123	TANK A, LI X, FOX E, et al. The convex mixture distribution: Granger causality for categorical time series[J]. SIAM Journal on Mathematics of Data Science, 2021, 3 (1): 83- 112. doi: 10.1137/20M133097X
124	GRANGER C W J. Testing for causality: a personal viewpoint[J]. Economic Dynamics and control, 1980, 2 (1): 329- 352.
125	GRANGER S. Social engineering fundamentals, part I: hacker tactics[EB/OF]. [2024-05-21]. https://www.social-engineer.org/wiki/archives/PenetrationTesters/Pentest-HackerTactics.html.
126	STOKES P A, PURDON PL. A study of problems encountered in Granger causality analysis from a neuroscience perspective[J]. Proceedings of the National Academy of Sciences, 2017, 114 (34): 7063- 7072.
127	MAZIARZ M. A review of the Granger causality fallacy[J]. Philosophical Economics, 2015, 8 (2): 86- 105.
128	GLYMOUR C, ZHANG K, SPIRTES P. Review of causal discovery methods based on graphical models[J]. Frontiers in Genetics, 2019, 10, 524. doi: 10.3389/fgene.2019.00524
129	任伟杰, 韩敏. 多元时间序列因果关系分析研究综述[J]. 自动化学报, 2021, 47 (1): 64- 78.
	REN W J, HAN M. Survey on causality analysis of multivariate time series[J]. Acta Automatica Sinica, 2021, 47 (1): 64- 78.
130	BERNANKE B S, BOIVIN J, ELIASZ P. Measuring the effects of monetary policy: a factor-augmented vector auto-regressive （FAVAR） approach[J]. Finance and Economic Discussion Series, 2005, 120 (1): 387- 422.
131	EICHLER M. Graphical modelling of multivariate time series[J]. Probability Theory and Related Fields, 2012, 153 (1/2): 233- 268.
132	BASU S, SHOJAIE A, MICHAILIDIS G. Network Granger causality with inherent grouping structure[J]. Machine Learning Research, 2015, 16 (1): 417- 53.
133	LANDMAN R, KORTELA J, JAMSA-JOUNELA S L. Fault propagation analysis by combining data-driven causal analysis and plant connectivity[C]//Proc. of the IEEE Emerging Technology and Factory Automation, 2014.
134	YUAN T, QIN S J. Root cause diagnosis of plant-wide oscillations using granger causality[J]. Journal of Process Control, 2012, 45 (15): 160- 165.
135	DI G J, GERONIMO G, ALBAI D B, et al. Topology-aware causal modeling for industrial process fault diagnosis[J]. IEEE Trans. on Industrial Informatics, 2015, 11 (3): 721- 730.
136	CHEN Q M, LANG X, LU S, et al. Detection and root cause analysis of multiple plant-wide oscillations using multivariate nonlinear chirp mode decomposition and multivariate granger causality[J]. Computers & Chemical Engineering, 2021, 147, 107231.
137	FLORENS J P, MOUCHART M. A note on noncausality[J]. Econometrica: Journal of the Econometric Society, 1982, 50 (3): 583- 591. doi: 10.2307/1912602
138	HENDERSON J, MICHAILIDIS G. Network reconstruction using nonparametric additive ODE models[J]. Plos One, 2014, 9 (4): e94003. doi: 10.1371/journal.pone.0094003
139	WU H L, LU T, XUE H Y, et al. Sparse additive ordinary differential equations for dynamic gene regulatory network modeling[J]. American Statistical Association, 2014, 109 (506): 700- 716. doi: 10.1080/01621459.2013.859617
140	CHEN S, SHOJAIE A, WITTEN D M. Network reconstruction from high- dimensional ordinary differential equations[J]. American Statistical Association, 2017, 112 (520): 1697- 1707. doi: 10.1080/01621459.2016.1229197
141	HUANG H, XU C X, YOO S, et al. Imbalanced time series classification for flight data analyzing with nonlinear granger causality learning[C]//Proc. of the 29th ACM International Conference on Information & Knowledge Management, 2020: 2533−2540.
142	SHOJAIE A, MICHAILIDIS G. Discovering graphical Granger causality using the truncating lasso penalty[J]. Bioinformatics, 2010, 26 (18): 517- 523. doi: 10.1093/bioinformatics/btq377
143	SHOJAIE A, BASU S, MICHAILIDIS G. Adaptive thresholding for reconstructing regulatory networks from time-course gene expression data[J]. Statistics in Biosciences, 2012, 4 (1): 66- 83. doi: 10.1007/s12561-011-9050-5
144	NICHOLSON WB, MATTESON DS, BIEN J. VARX-L: structured regularization for large vector autoregressions with exogenous variables[J]. International Journal of Forecasting, 2017, 33 (3): 627- 651. doi: 10.1016/j.ijforecast.2017.01.003
145	FOX E, SUDDERTH EB, JORDAN MI, et al. Bayesian nonparametric inference of switching dynamic linear models[J]. IEEE Trans. on Signal Processing, 2011, 59 (4): 1569- 1585. doi: 10.1109/TSP.2010.2102756
146	BAI P, SAFIKHANI A, MICHAILIDIS G. Multiple change points detection in low rank and sparse high dimensional vector autoregressive models[J]. IEEE Trans. on Signal Processing, 2020, 68, 3074- 3089. doi: 10.1109/TSP.2020.2993145
147	TANK A, FOX EB, SHOJAIE A. Identifiability and estimation of structural vector autoregressive models for subsampled and mixed-frequency time series[J]. Biometrika, 2019, 106 (2): 433- 452. doi: 10.1093/biomet/asz007
148	寻凯, 尹洪, 刘海英. 不同绞向组合覆冰分裂导线稳定性及其舞动特性[J]. 高电压技术, 2021, 47 (7): 2506- 2513.
	XUN K, YIN H, LIU H Y. Stability and galloping characteristic of iced bundled conductor with the combination in various directions of lay[J]. High Voltage Engineering, 2021, 47 (7): 2506- 2513.
149	李书进, 张志聪, 孔凡, 等. 周期与色噪声联合作用下分数阶Duffing振子非平稳响应的无记忆方法[J]. 振动工程学报, 2023, 36 (4): 923- 933.
	LI S J, ZHANG Z C, KONG F, et al. Memory free method for non-stationary response of fractional order Duffing oscillators under the combined action of periodic and colored noise[J]. Journal of Vibration Engineering, 2023, 36 (4): 923- 933.
150	LI Y, YU R, SHAHABI C, et al. Diffusion convolutional recurrent neural network: data-driven traffic forecasting. [EB/OL]. [2024-05-28]. https://arxiv.org/abs/1707.01926.
151	YU R, ZHENG S, ANANDKUMAR A, et al. Long-term forecasting using tensor-train RNNs[EB/OL]. [2024-05-28]. https://arxiv.org/abs/1711.00073.
152	TAO Y Z, MA L, ZHANG W Z, et al. Hierarchical attention-based recurrent highway networks for time series prediction [EB/OL]. [2024-05-28]. https://arxiv.org/abs/1806.00685.
153	DENG Z Z, ZHENG X L. HU T, et al. Deep causal learning: representation, discovery and inference[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2211.03374.
154	VOWELS M J, CAMGOZ N C, BOWDEN R. D’ya like DAGs? A survey on structure learning and causal discovery. ACM Computing Surveys[J]. ACM Computing Surveys, 2022, 55 (4): 1- 36.
155	ZHENG X, ARAGAM B, RAVIKUMA P K, et al. Dags with no tears: Continuous optimization for structure learning[C]//Proc. of the 32nd Annual Conference on Neural Information Processing Systems, 2018: 9492−9503.
156	NG I, ZHU S Y, CHEN Z T. et al. A graph autoencoder approach to causal structure learning[EB/OL]. [2024-05-28]. https://arxiv.org/abs/1911.07420.
157	YU Y, CHEN J, GAO T, et al. DAG-GNN: DAG structure learning with graph neural networks[C]//Proc. of the International Conference on Machine Learning, 2019: 7154−7163.
158	LACHAPELLE S, BROUILLARD P, DELEU T. Gradient-based neural DAG learning[C]//Proc. of the International Conference on Learning Representations, 2020.
159	YU Y, GAO T, YI N Y, et al. DAGs with no curl: an efficient DAG structure learning approach[C]//Proc. of the International Conference on Machine Learning, 2021: 12156−12166.
160	ABADIE A, IMBENS G W. Matching on the estimated propensity score[J]. Econometrica, 2016, 84 (2): 781- 807. doi: 10.3982/ECTA11293
161	KE N R, BILANIUK O, GOYAL A, et al. Learning neural causal models from unknown interventions [EB/OL]. [2024-05-28]. https://arxiv.org/abs/1910.01075.
162	MORAFFAH R, MORAFFAH B, KARAMI M, et al. Causal adversarial network for learning conditional and interventional distributions[EB/OL]. [2024-05-21]. https://arxiv.org/abs/2008.11376.
163	SAUTER A W, BOTTEGHI N, ACAR E, et al. CORE: towards scalable and efficient causal discovery with reinforcement learning[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2401.16974.
164	LIPPE P, COHEN T, GAVVES E. Efficient neural causal discovery without acyclicity constraints[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2107.10483.
165	RICHTER R, BHAMIDI S, MUKHERJEE S. Improved baselines for causal structure learning on interventional data[J]. Statistics and Computing, 2023, 33 (5): 93. doi: 10.1007/s11222-023-10257-9
166	KORTE B H, VYGEN J, KORTE B, et al. Combinatorial optimization[M]. Berlin: Springer, 2011.
167	GOUDET O, KALAINATHAN D, CAILLOU P, et al. Learning functional causal models with generative neural networks[EB/OL]. [2024-05-28]. https://arxiv.org/abs/1709.05321.
168	KALAINATHAN D. Generative neural networks to infer causal mechanisms: algorithms and applications[D]. Paris: Paris-Saclay University, 2019.
169	KALTENPOTH D, VREEKEN J. Nonlinear causal discovery with latent confounders[C]//Proc. of the International Conference on Machine Learning, 2023: 15639−15654.
170	ASHMAN M, MA C, HILMKIL A, et al. Causal reasoning in the presence of latent confounders via neural ADMG learning [EB/OL]. [2024-05-28]. https://arxiv.org/pdf/2303.12703.
171	RUNGE J, BATHIANY S, BOLLT E, et al. Inferring causation from time series in Earth system sciences[J]. Nature communications, 2019, 10 (1): 2553. doi: 10.1038/s41467-019-10105-3
172	DANKS D, PLIS S. Learning causal structure from under-sampled time series [C]//Proc. of the 27th Conference on Neural Information Processing Systems, 2013.
173	HYTTINEN A, PLIS S, JARVISALO M, et al. Causal discovery from subsampled time series data by constraint optimization [C]//Proc. of the Conference on Probabilistic Graphical Models, 2016: 216−227.
174	KHANNA S, TAN V Y. Economy statistical recurrent units for inferring nonlinear granger causality[C]//Proc. of the International Conference on Learning Representations, 2020.
175	MARCINKEVICS R, VOGT J E. Interpretable models for Granger causality using self-explaining neural networks [EB/OL]. [2024-05-28]. https://arxiv.org/abs/2101.07600.
176	LI H M, YU S J, PRINCIPE J. Causal recurrent variational autoencoder for medical time series generation[C]//Proc. of the AAAI Conference on Artificial Intelligence, 2023: 8562−8570.
177	SINGH R, WU A P, BERGER B. Granger causal inference on DAGs identifies genomic loci regulating transcription [EB/OL]. [2024-05-28]. https://arxiv.org/abs/2210.10168.
178	SUN X Y, SCHULTE O, LIU G L, et al. NTS-NOTEARS: Learning nonparametric DBNs with prior knowledge[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2109.04286.
179	GONG W B, JENNINGS J, ZHANG C, et al. Rhino: Deep causal temporal relationship learning with history-dependent noise [EB/OL]. [2024-05-28]. https://arxiv.org/abs/2210.14706.
180	DAI E, CHEN J. 2022. Graph augmented normalizing flows for anomaly detection of multiple time series[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2202.07857.
181	CHU Y F, WANG X W, MA J X, et al. 2020. Inductive granger causal modeling for multivariate time series[C]//Proc. of the IEEE International Conference on Data Mining, 2020: 972−977.
182	LÖWE S, MADRAS D, ZEMEL R, et al. Amortized causal discovery: Learning to infer causal graphs from time-series data[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2006.10833.
183	KE N R, WANG J, MITROVIC J, et al. Amortized learning of neural causal representations[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2008.09301.
184	GAO T, BHATTACHARJYA D, NELSON E, et al. Learning nonparametric DAGs from interventional dynamic data[C]//Proc. of the International Conference on Machine Learning, 2022: 6988−7001.
185	LIU C X, KUANG K. Causal structure learning for latent intervened nonstationary data[C]//Proc. of the International Conference on Machine Learning, 2023: 21756−21777.
186	CHENG Y X, YANG R Z, XIAO T X, et al. Cuts: Neural causal discovery from irregular time-series data[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2302.07458.
187	WANG B J, JENNINGS J, GONG W B. Neural structure learning with stochastic differential equations[EB/OL]. [2024-05-28]. https://arxiv.org/abs/2311.03309.
188	BARNETT L, SETH A K. The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference[J]. Journal of neuroscience methods, 2014, 223, 50- 68. doi: 10.1016/j.jneumeth.2013.10.018
189	CHIKHAOUI B, CHIAZZARO M, WANG S R. A new granger causal model for influence evolution in dynamic social networks: the case of DBLP[C]//Proc. of the AAAI Conference on Artificial Intelligence, 2015: 51-57.
190	NAUTA M, BUCUR D, SEIFERT C. Causal discovery with attention-based convolutional neural networks[J]. Machine Learning and Knowledge Extraction, 2019, 1 (1): 312- 340. doi: 10.3390/make1010019
191	SCHREIBER T. Measuring information transfer[J]. Physical Review Letters, 2000, 85 (2): 461- 464. doi: 10.1103/PhysRevLett.85.461
192	FISHER R A. On the “probable error” of a coefficient of correlation deduced from a small sample[J]. Metron, 1921, 1 (4): 3- 32.
193	FIELLER E C, HARTLEY H O, PEARSON E S. Tests for rank correlation coefficients[J]. Biometrika, 1957, 44 (3/4): 470- 481. doi: 10.2307/2332878
194	FISHER R A. Statistical methods, experimental design, and scientific inference [M]. New York: Oxford University Press, 1990.
195	ZHANG L, WANG L. Optimization of site investigation program for reliability assessment of undrained slope using Spearman rank correlation coefficient[J]. Computers and Geotechnics, 2023, 155, 105208. doi: 10.1016/j.compgeo.2022.105208
196	KENDALL M, GIBBONS J D. Rank correlation methods[M]. New York: Oxford University Press, 1990.
197	徐维超. 相关系数研究综述[J]. 广东工业大学学报, 2012, 29 (3): 12- 17.
	XU W C. A Review on Correlation Coefficients[J]. Journal of Guangdong University of Technology, 2012, 29 (3): 12- 17.
198	HUANG Z L, QIN G S. Influence function-based confidence intervals for the Kendall rank correlation coefficient[J]. Computational Statistics, 2023, 38 (2): 1041- 1055. doi: 10.1007/s00180-022-01267-8
199	LANDMAN R, KORTELA J, SUN Q, et al. Fault propagation analysis of oscillations in control loops using data-driven causality and plant connectivity[J]. Computers & Chemical Engineering, 2014, 71, 446- 456.
200	赵西亮. 基本有用的计量经济学[M]. 北京: 北京大学出版社, 2018. ZHAO X L. Mostly useful science of econometrics[M]. Beijng: Peking University Press, 2017.
201	PAGE L, BRIN S, MOTWANI R, et al. The PageRank citation ranking: bringing order to the web[R]. San Francisco: Stanford University, 1998.
202	TARJAN R. Depth-first search and linear graph algorithms[J]. SIAM Journal on Computing, 1972, 1 (2): 146- 160. doi: 10.1137/0201010
203	MOORE E F. The Shortest path through a maze[C]//Proc. of the International Symposium on the Theory of Switching, 1957: 285−292.
204	FOUSS F, PIROTTE A, RENDERS J M, et al. Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation[J]. IEEE Trans. on Knowledge and Data Engineering, 2007, 19 (3): 355- 369. doi: 10.1109/TKDE.2007.46
205	KIM M, SUMBALY R, SHAH S. Root cause detection in a service-oriented architecture[J]. ACM SIGMETRICS Performance Evaluation Review, 2013, 41 (1): 93- 104. doi: 10.1145/2494232.2465753
206	BENNACER L, AMIRAT Y, CHIBANI A, et al. Self-diagnosis technique for virtual private networks combining Bayesian networks and case-based reasoning[J]. IEEE Trans. on Automation Science and Engineering, 2014, 12 (1): 354- 366.
207	DOWNS J J, VOGEL E F. A plantwide industrial process control problem[J]. Computers & Chemical Engineering, 1993, 17 (3): 245- 255.
208	MARWEDE N, ROHR M, HOORN A V, et al. Automatic failure diagnosis support in distributed large-scale software systems based on timing behavior anomaly correlation[C]//Proc. of the 13th European Conference on Software Maintenance and Reengineering, 2009: 47−58.
209	COHEN I, CHASE J S, GOLDSZMIDT M, et al. Correlating instrumentation data to system states: a building block for automated diagnosis and control[C]//Proc. of the 6th Symposium on Operating Systems Design and Implementation, 2004.
210	KANDULA S, MAHAJAN R, VERKAIK P, et al. Detailed diagnosis in enterprise networks[J]. ACM SIGCOMM Computer Communication, 2009, 39 (4): 243- 254. doi: 10.1145/1594977.1592597
211	THALHEIM J, RODRIGUESA, AKKUS I E, et al. Sieve: actionable insights from monitored metrics in distributed systems [C]//Proc. of the 18th ACM/IFIP/USENIX Middleware Conference, 2017: 14−27.
212	JAYATHILAKA H, KRINTZ C, WOLSKI R. Performance monitoring and root cause analysis for cloud-hosted web applications [C]//Proc. of the 26th International Conference on World Wide Web, 2017: 469−478.
213	CHEN H S, YAN Z B, ZHANG X L, et al. Root cause diagnosis of process faults using conditional granger causality analysis and maximum spanning tree[J]. IFAC-Papers OnLine, 2018, 51 (18): 381- 386. doi: 10.1016/j.ifacol.2018.09.330
214	MARIANI L, MONNI C, PEZZE M, et al. Fault localization in cloud environments using causal correlation and machine learning[J]. IEEE Trans. on Cloud Computing, 2020, 8 (4): 1123- 1136.
215	NGUYEN H, TAN Y M, GU X H. PAL: propagation-aware anomaly localization for cloud hosted distributed applications [EB/OL]. [2024-05-28]. https://dance.csc. ncsu.edu/papers/slaml11.pdf.
216	NGUYEN H, SHEN Z M, TAN Y M, et al. Fchain: toward black box online fault localization for cloud systems[C]//Proc. of the IEEE 33nd International Conference on Distributed Computing Systems, 2013: 21−30.
217	陈薇. 面向不完全观察数据的混淆因子检测与因果结构学习研究[D]. 广州: 广东工业大学, 2020.
	CHEN W. Confounding factor detection and causal structure learning study for incomplete observed data[D]. Guangzhou: Guangdong University of Technology, 2010.
218	ZHENG Y. Methodologies for cross-domain data fusion: an overview[J]. IEEE Trans. on Big Data, 2015, 1 (1): 16- 34. doi: 10.1109/TBDATA.2015.2465959
219	CLIVIO O, FALCK F, LEHMANN B, et al. Neural score matching for high-dimensional causal inference[C]//Proc. of the International Conference on Artificial Intelligence and Statistics, 2022: 7076−7110.
220	BAREINBOIM E, TIAN J, PEARL J. Recovering from selection bias in causal and statistical inference[C]//Proc. of the Probabilistic and Causal Inference, 2022: 433450.
221	SCHEUTZ M. Computational versus causal complexity[J]. Minds and Machines, 2001, 11 (4): 543- 566. doi: 10.1023/A:1011855915651
222	ZHANG K, SCHOLKOPF B, SPIRTES P, et al. Learning causality and causality-related learning: some recent progress[J]. National Science Review, 2018, 5 (1): 26- 29. doi: 10.1093/nsr/nwx137
223	FORRE P, MOOIJ J M. Constraint-based causal discovery for non-linear structural causal models with cycles and latent confounders[EB/OL]. [2024-05-28]. https://arxiv.org/abs/1807.03024.
224	LI H F, HAI M, TANG W X. Prior knowledge-based causal inference algorithms and their applications for China COVID-19 analysis[J]. Mathematics, 2022, 10 (19): 3568. doi: 10.3390/math10193568
225	孟媛. 互联网应用性能异常的根因定位研究[D]. 北京: 清华大学, 2021.
	MENG Y. Study on the root cause localization of abnormal internet application performance[D]. Beijing: Tsinghua University, 2021.
226	赵森栋, 刘挺. 因果关系及其在社会媒体上的应用研究综述[J]. 软件学报, 2014, 25 (12): 2733- 2752.
	ZHAO S D, LIU T. Review of causality and its application in social media[J]. Journal of Software, 2014, 25 (12): 2733- 2752.

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

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