扩展了因果图模型，支持含循环因果关系的潜变量系统建模。
$σ$-Maximal Ancestral Graphs
- 提出σ-MAGs，将MAG框架推广到允许循环因果的有向图。
- 证明σ-MAG能准确表示含潜变量的循环系统，且保持马尔可夫等价性特征。
- 适用于存在反馈环的复杂因果系统分析，如生物网络或社会系统。
最大祖先图（MAGs）为包含潜变量和选择变量的有向无环图（DAGs）提供抽象表示，编码祖先关系与d-分离信息。该表示被用于证明因果发现算法FCI的完备性与正确性，并推导其输出的do-演算。然而，MAG的一个固有限制是无法处理循环因果关系。本文提出并研究一类新图形对象——σ-最大祖先图（σ-MAGs），其作为含潜变量的可能含循环的有向图（DGs）的抽象表示，类似于MAG对DAG的表示。我们研究了σ-MAG的性质，并给出了其马尔可夫等价类的刻画。
原文摘要 · Abstract (English)
Maximal Ancestral Graphs (MAGs) provide an abstract representation of Directed Acyclic Graphs (DAGs) with latent (selection) variables. These graphical objects encode information about ancestral relations and d-separations of the DAGs they represent. This abstract representation has been used amongst others to prove the soundness and completeness of the FCI algorithm for causal discovery, and to derive a do-calculus for its output. One significant inherent limitation of MAGs is that they rule out the possibility of cyclic causal relationships. In this work, we address that limitation. We introduce and study a class of graphical objects that we coin ''$σ$-Maximal Ancestral Graphs'' (''$σ$-MAGs''). We show how these graphs provide an abstract representation of (possibly cyclic) Directed Graphs (DGs) with latent (selection) variables, analogously to how MAGs represent DAGs. We study the properties of these objects and provide a characterization of their Markov equivalence classes.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。