Context-Specific Independence in Bayesian Networks
Context-Specific Independence in Bayesian Networks
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发表时间：
1996-08
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通讯作者：
Craig Boutilier;N. Friedman;M. Goldszmidt;D. Koller
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作者：
Craig Boutilier;N. Friedman;M. Goldszmidt;D. Koller
贝叶斯网络提供了一种定性表示分布的条件独立属性的语言，这允许分布的自然和紧凑的表示，简化了知识获取，并支持有效的推理算法。然而，众所周知，在贝叶斯网络结构中，我们无法定性地捕获某些独立性：仅在某些上下文中成立的独立性，即，给定某些变量的特定值分配，在本文中，我们基于节点条件概率表（CPTS）中的规则性，提出了上下文特定独立性（CSI）的正式概念。我们提出了一种技术，类似于（并基于）d-分离，用于确定何时在给定的网络中保持这种独立性。然后，我们专注于一个特定的定性表示方案-树结构的CPT-捕捉CSI。我们建议的方式，这种表示可以用来支持有效的推理算法，特别是，我们提出了一个结构分解的结果网络，可以提高聚类算法的性能，和一个替代算法的基础上开始条件。
Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution, This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables, In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme--tree-structured CPTs-- for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms, in particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on outset conditioning.