论文标题
p-d分开 - 在因果网络中表达依赖/独立关系的概念
p-d-Separation -- A Concept for Expressing Dependence/Independence Relations in Causal Networks
论文作者
论文摘要
Spirtes，Glymour和Scheines提出了一种猜想，即直接依赖测试和正面的会议测试足以解释Pearl D-Separeation适用的联合概率分布（贝叶斯网络）的定向无环形分解（贝叶斯网络）。后来，这种猜想是珍珠和维尔马结果的直接结果。本文旨在通过利用P-d分隔的概念（部分依赖性分离）来以新的方式证明这种猜想。虽然Pearl的D分隔与贝叶斯网络合作，但P-D分解旨在适用于因果网络：这是部分面向的网络，仅针对这些边缘提供了方向，这些网络表现出统计确认的因果影响，而无方向性的边缘表达了直接影响，而无需确定责任的方向。还出于证明这种猜想的有效性的特定方式，这是一种用于构建所有有针对性的无环形图（DAG）的算法。引入了部分定向图（POG）的概念，并在此图中定义了p-d分隔的概念。证明POG内的p-d分离等效于所有派生的dag中的d分离。
Spirtes, Glymour and Scheines formulated a Conjecture that a direct dependence test and a head-to-head meeting test would suffice to construe directed acyclic graph decompositions of a joint probability distribution (Bayesian network) for which Pearl's d-separation applies. This Conjecture was later shown to be a direct consequence of a result of Pearl and Verma. This paper is intended to prove this Conjecture in a new way, by exploiting the concept of p-d-separation (partial dependency separation). While Pearl's d-separation works with Bayesian networks, p-d-separation is intended to apply to causal networks: that is partially oriented networks in which orientations are given to only to those edges, that express statistically confirmed causal influence, whereas undirected edges express existence of direct influence without possibility of determination of direction of causation. As a consequence of the particular way of proving the validity of this Conjecture, an algorithm for construction of all the directed acyclic graphs (dags) carrying the available independence information is also presented. The notion of a partially oriented graph (pog) is introduced and within this graph the notion of p-d-separation is defined. It is demonstrated that the p-d-separation within the pog is equivalent to d-separation in all derived dags.
