Characteristic imset: a simple algebraic representative of a Bayesian network structure
Characteristic imset: a simple algebraic representative of a Bayesian network structure
复制标题
特征imset：贝叶斯网络结构的简单代数表示
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
S. Lindner
中科院分区：
文献类型：
--
作者：
M. Studen;R. Hemmecke;S. Lindner
首先，我们回顾一下（student y， Vomlel和Hemmecke， 2010）中提出的学习贝叶斯网络（BN）结构的代数和几何方法的基本思想：用某个唯一确定的向量表示每个BN结构。最初的建议是使用所谓的标准集，它是一个以整数为分量的向量，作为BN结构的代数代表。在本文中，我们提出了一个更简单的代数表示，称为特征集。它是一个0-1的向量，它是由一个变换得到的。这意味着每一个合理的质量标准都是特征集的一个函数。特征集更接近于图形描述：我们建立了一个与任何没有ags的链图的简单关系，该链图否认BN结构。特别是，我们对本质图的关系感兴趣，本质图是一个经典的图形BN结构代表。最后，我们讨论了两个特殊的情况，其中使用特征集特别简化了事情：学习可分解模型和（无向）森林。
First, we recall the basic idea of an algebraic and geometric approach to learning a Bayesian network (BN) structure proposed in (Studen y, Vomlel and Hemmecke, 2010): to represent every BN structure by a certain uniquely determined vector. The original proposal was to use a so-called standard imset which is a vector having integers as components, as an algebraic representative of a BN structure. In this paper we propose an even simpler algebraic representative called the characteristic imset. It is 0-1-vector obtained from the standard imset by an ane transformation. This implies that every reasonable quality criterion is an ane function of the characteristic imset. The characteristic imset is much closer to the graphical description: we establish a simple relation to any chain graph without ags that denes the BN structure. In particular, we are interested in the relation to the essential graph, which is a classic graphical BN structure representative. In the end, we discuss two special cases in which the use of characteristic imsets particularly simplies things: learning decomposable models and (undirected) forests.