Decomposable graphical models, also known as perfect DAG models, play a fundamental role in standard approaches to probabilistic inference via graph representations in modern machine learning and statistics. However, such models are limited by the assumption that the data-generating distribution does not entail strictly context-specific conditional independence relations. The family of staged tree models generalizes DAG models so as to accommodate context-specific knowledge. We provide a new characterization of perfect discrete DAG models in terms of their staged tree representations. This characterization identifies the family of balanced staged trees as the natural generalization of discrete decomposable models to the context-specific setting.
翻译:可分解的图形模型,又称完美的DAG模型,在通过现代机器学习和统计中的图示表达方式进行概率推论的标准方法中发挥着根本作用,但是,这些模型受到以下假设的限制:数据生成分布并不涉及严格针对具体情况的有条件独立关系。分阶段的树模型的组合将DAG模型加以概括,以适应具体情况的知识。我们从分阶段的树木表述角度对完美的离散的DAG模型作了新的定性。这种定性将平衡的分阶段树木组合确定为离散、不相容的模型与特定背景环境的自然概括。