提出可分离图模型新框架，统一处理反馈、潜变量等复杂依赖关系。
Characterizing and Identifying Separable Graphical Models
- 基于混合图的顶点分离定义新型图模型，支持反馈与潜变量建模
- 证明可分离图与本质上可分离图存在多种等价刻画方式
- 给出本质可分离图的规范表示及识别算法，适用于复杂因果推断场景
我们研究一类广义图模型，其独立性关系对应于含有有向、无向和双箭头边的混合图中的顶点分离，能够编码反馈、潜变量和选择机制引发的独立结构。特别地，我们引入可分离图（separable graphs），其中每条缺失边均对应其端点间存在分离集；以及本质上可分离图（essentially separable graphs），即与某可分离图分离等价的图。我们证明这类模型包含许多现有图模型家族，并提供了可分离图与本质上可分离图的多种刻画方法。此外，我们给出了可分离图分离等价性的多重刻画：一种基于普通图性质的图形化刻画，扩展了对特定子族的早期结果；另一种仅依赖图分离性质的分离化刻画。最后，我们为本质上可分离图的等价类提供了规范表示，并在合理假设下设计出识别任意本质上可分离图等价类的算法。
原文摘要 · Abstract (English)
We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback, latent and selection mechanisms. In particular, we introduce separable graphs, in which each missing edge implies the existence of a separating set for its endpoints, and essentially separable graphs, those graphs separation equivalent to a separable graph. We show that these models include many existing graph families used to define graphical models an provide several characterizations of separable graphs and essentially separable graphs. We also provide multiple characterizations of separation equivalence for separable graphs. One is a graphical characterization in terms of ordinary graph properties, extending earlier results for specific subfamilies Another is a separational characterization depending only on graph separation properties. Finally, we provide a canonical representation for the equivalence classes of essentially separable graphs and develop an algorithm that, under suitable assumptions, identifies the equivalence class of any essentially separable graph.
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