论文标题
无条件等效的贝叶斯网络的变革表征
A Transformational Characterization of Unconditionally Equivalent Bayesian Networks
论文作者
论文摘要
我们考虑将贝叶斯网络表征到无条件等效的问题，即，当定向无环形图（DAGS）具有相同的无条件$ d $分离式语句。每个无条件的等效类（UEC）都用一个无方向的图形表示，该图形编码了类的成员。通过这种结构，我们提供了无条件等价的变革性表征。也就是说，我们显示，只有一个有限的指定移动序列可以将两个DAG在同一UEC中，并且仅当一个DAG在另一个DAG中。我们还将此特征扩展到代表UEC中Markov等效类（MEC）的基本图。 UEC分配了MEC的空间，并且可以从边际独立性测试中估算。因此，无条件等价的表征在涉及搜索贝叶斯网络空间的方法中应用。
We consider the problem of characterizing Bayesian networks up to unconditional equivalence, i.e., when directed acyclic graphs (DAGs) have the same set of unconditional $d$-separation statements. Each unconditional equivalence class (UEC) is uniquely represented with an undirected graph whose clique structure encodes the members of the class. Via this structure, we provide a transformational characterization of unconditional equivalence; i.e., we show that two DAGs are in the same UEC if and only if one can be transformed into the other via a finite sequence of specified moves. We also extend this characterization to the essential graphs representing the Markov equivalence classes (MECs) in the UEC. UECs partition the space of MECs and are easily estimable from marginal independence tests. Thus, a characterization of unconditional equivalence has applications in methods that involve searching the space of MECs of Bayesian networks.
