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=== 基于约束的因果发现方法 ===
=== 基于约束的因果发现方法 ===
基于约束的因果发现方法主要基于独立性和条件独立性检测判断变量之间的统计关系，并在一定的假设下先获得无向因果图。之后利用V-structure和一系列方向传播规则对因果图中的无向边进行方向传播。其经典方法包括PC<ref>Spirtes, P., Glymour, C. N., Scheines, R., & Heckerman, D. (2000). Causation, prediction, and search. MIT press.</ref>算法，能够处理隐变量（混淆变量）的FCI<ref>Spirtes, P., Meek, C., & Richardson, T. (1995, August). Causal inference in the presence of latent variables and selection bias. In Proceedings of the Eleventh conference on Uncertainty in artificial intelligence (pp. 499-506).</ref>算法，以及能够处理异构数据的CD-NOD<ref>Huang, B., Zhang, K., Zhang, J., Ramsey, J. D., Sanchez-Romero, R., Glymour, C., & Schölkopf, B. (2020). Causal Discovery from Heterogeneous/Nonstationary Data. J. Mach. Learn. Res., 21(89), 1-53.</ref>算法。
=== 基于评分的因果发现方法 ===
=== 基于评分的因果发现方法 ===
基于评分的方法通过对候选模型（即候选因果图）进行评分的方式，来选取评分最高的因果图作为结果。经典方法包括GES<ref>Chickering, D. M. (2002). Optimal structure identification with greedy search. Journal of machine learning research, 3(Nov), 507-554.</ref>以及一系列通过改变评分函数来适应不同任务的扩展方法，例如基于通用评分函数的因果发现方法<ref>Huang, B., Zhang, K., Lin, Y., Schölkopf, B., & Glymour, C. (2018, July). Generalized score functions for causal discovery. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (pp. 1551-1560).</ref>。此外，对于实际情况中Faithfulness假设不满足的情景，Exact Search<ref>Ng, Ignavier, Yujia Zheng, Jiji Zhang, and Kun Zhang. "Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions." ''Advances in Neural Information Processing Systems'' 34 (2021): 20308-20320.</ref>可提供可靠的马尔科夫等价类。
=== 基于约束性函数因果模型的因果发现方法 ===
=== 基于约束性函数因果模型的因果发现方法 ===
基于约束性函数因果模型的因果方法通过假设结果和原因之间的函数关系类别，从而判断其间的方向。经典方法包括线性非高斯无环模型<ref>Shimizu, S., Hoyer, P. O., Hyvärinen, A., Kerminen, A., & Jordan, M. (2006). A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7(10).</ref>，加性噪声模型<ref>Hoyer, P. O., Janzing, D., Mooij, J. M., Peters, J., & Schölkopf, B. (2008, December). Nonlinear causal discovery with additive noise models. In NIPS (Vol. 21, pp. 689-696).</ref>和后非线性模型<ref>Zhang, K., & Hyvärinen, A. (2009, June). On the Identifiability of the Post-Nonlinear Causal Model. In 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009) (pp. 647-655). AUAI Press.</ref>。近期通过对混合函数进行限制从而得到非线性独立成分分析的可识别性的理论<ref>Zheng, Yujia, Ignavier Ng, and Kun Zhang. "On the Identifiability of Nonlinear ICA: Sparsity and Beyond." ''arXiv preprint arXiv:2206.07751'' (2022).</ref>也为通用的非线性的因果发现提供了新的方法。
=== 因果隐表征学习 ===
=== 因果隐表征学习 ===
因果隐表征学习专注于隐变量与观测变量间的关系以及隐变量间的关系，经典工作包括GIN<ref>Xie, Cai, Huang, Glymour, Hao, Zhang, "Generalized Independent Noise Condition for Estimating Linear Non-Gaussian Latent Variable Causal Graphs," NeurIPS 2020</ref>以及层级化隐变量学习<ref>Feng Xie, Biwei Huang, Zhengming Chen, Yangbo He, Zhi Geng, Kun Zhang, "Estimation of Linear Non-Gaussian Latent Hierarchical Structure," accepted to ''International Conference on Machine Learning (ICML) 2022''</ref>。
=== 因果发现工具：causal-learn ===
=== 因果发现工具：causal-learn ===