贝叶斯网络包含性的刻画
On characterizing Inclusion of Bayesian Networks
摘要：
每个有向无环图（DAG）在一个有限的非空变量集（=节点）N上诱导一个独立模型，这是一个N上的条件独立语句列表。包含问题是如何（用图形术语）表征由DAG K诱导的模型中的所有独立语句是否都在由第二个DAG L诱导的模型中。Meek（1997）证明了这一包含成立当且仅当存在一个从L到K的DAG序列，使得只有某些“合法的”箭头反转和“合法的”箭头相加操作才能得到序列中的下一个DAG.本文给出了DAG模型包含的几个特征，并在DAG模型K和L至多有一个邻接不同的情况下验证了Meek猜想.作为热身，严格证明著名的图形特征的等价性的DAG，这是一个高度相关的问题，给出。
英文摘要：
Every directed acyclic graph (DAG) over a finite non-empty set of variables (= nodes) N induces an independence model over N, which is a list of conditional independence statements over N.The inclusion problem is how to characterize (in graphical terms) whether all independence statements in the model induced by a DAG K are in the model induced by a second DAG L. Meek (1997) conjectured that this inclusion holds iff there exists a sequence of DAGs from L to K such that only certain 'legal' arrow reversal and 'legal' arrow adding operations are performed to get the next DAG in the sequence.In this paper we give several characterizations of inclusion of DAG models and verify Meek's conjecture in the case that the DAGs K and L differ in at most one adjacency. As a warming up a rigorous proof of well-known graphical characterizations of equivalence of DAGs, which is a highly related problem, is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
