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首页> 外文期刊>International Journal of Uncertainty, Fuzziness, and Knowledge-based Systems >Thinning a Triangulation of a Bayesian Network or Undirected Graph to Create a Minimal Triangulation
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Thinning a Triangulation of a Bayesian Network or Undirected Graph to Create a Minimal Triangulation

机译：细化贝叶斯网络或无向图的三角剖分以创建最小三角剖分

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摘要

In one procedure for finding the maximal prime decomposition of a Bayesian network or undirected graphical model, the first step is to create a minimal triangulation of the network, and a common and straightforward way to do this is to create a triangulation that is not necessarily minimal and then thin this triangulation by removing excess edges. We show that the algorithm for thinning proposed in several previous publications is incorrect. A different version of this algorithm is available in the R package gRbase, but its correctness has not previously been proved. We prove that this version is correct and provide a simpler version, also with a proof. We compare the speed of the two corrected algorithms in three ways and find that asymptotically their speeds are the same, neither algorithm is consistently faster than the other, and in a computer experiment the algorithm used by gRbase is faster when the original graph is large, dense, and undirected, but usually slightly slower when it is directed.
机译：在查找贝叶斯网络或无向图形模型的最大素分解的一个过程中，第一步是创建网络的最小三角剖分，而实现这一目标的常见而直接的方法是创建不一定最小的三角剖分然后通过去除多余的边缘来使三角形划分变薄。我们证明了以前的几篇出版物中提出的细化算法是不正确的。 R包gRbase中提供了该算法的不同版本，但是以前尚未证明其正确性。我们证明该版本正确，并提供了更简单的版本并附带证明。我们以三种方式比较了两种校正算法的速度，发现它们的渐近速度相同，两种算法的一致性都比另一种算法快，并且在计算机实验中，当原始图较大时，gRbase使用的算法更快，密集且无方向，但定向时通常稍慢。

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