Redefining the Shortest Path Problem Formulation of the Linear Non-Gaussian Acyclic Model: Pairwise Likelihood Ratios, Prior Knowledge, and Path Enumeration
重构 LiNGAM 的最短路径表述：成对似然比、先验知识与路径枚举AI 解读 ↓
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重构 LiNGAM 的最短路径表述：成对似然比、先验知识与路径枚举
- 研究问题
- 如何改进 LiNGAM 最短路径框架，减少独立性度量的调参需求、纳入因果顺序先验，并从路径分布获取结构信息？
- 方法与思路
- 作者用成对似然比替代近邻互信息估计，通过节点跳过策略排除违反先验顺序的路径，并分析因果排序路径的分布。
- 材料陈述的贡献
- 摘要称三项改进减少调参、增强先验输入灵活性，并可推测潜在混杂与稀疏性；所述基准实验报告了性能改善。
- 阅读关注点
- 应核对似然比替代的理论依据、潜在混杂下的适用范围、路径统计的解释，以及基准比较的调参与计算成本。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未给出完整识别条件，不能据此认定方法普遍解决潜在混杂问题。
原文摘要
Effective causal discovery is essential for learning the causal graph from observational data. The linear non-Gaussian acyclic model (LiNGAM) operates under the assumption of a linear data generating process with non-Gaussian noise in determining the causal graph. Its assumption of unmeasured confounders being absent, however, poses practical limitations. In response, empirical research has shown that the reformulation of LiNGAM as a shortest path problem (LiNGAM-SPP) addresses this limitation. Within LiNGAM-SPP, mutual information is chosen to serve as the measure of independence. A challenge is introduced - parameter tuning is now needed due to its reliance on kNN mutual information estimators. The paper proposes a threefold enhancement to the LiNGAM-SPP framework. First, the need for parameter tuning is eliminated by using the pairwise likelihood ratio in lieu of kNN-based mutual information. This substitution is validated on a general data generating process and benchmark real-world data sets, outperforming existing methods especially when given a larger set of features. The incorporation of prior knowledge is then enabled by a node-skipping strategy implemented on the graph representation of all causal orderings to eliminate violations based on the provided input of relative orderings. Flexibility relative to existing approaches is achieved. Last among the three enhancements is the utilization of the distribution of paths in the graph representation of all causal orderings. From this, crucial properties of the true causal graph such as the presence of unmeasured confounders and sparsity may be inferred. To some extent, the expected performance of the causal discovery algorithm may be predicted. The refinements above advance the practicality and performance of LiNGAM-SPP, showcasing the potential of graph-search-based methodologies in advancing causal discovery.