利用状态相似性降低BN2O网络计算复杂性度
Computational Complexity Reduction for BN2O Networks Using Similarity of States
摘要：
虽然在一般的贝叶斯信念网络的概率推理是一个NP难问题，推理的计算时间可以减少在大多数实际情况下，通过利用领域知识，并通过在知识表示近似。本文介绍了状态相似性的性质以及基于此性质的近似知识表示和推理的一种新方法。我们定义一个节点的两个或多个状态是相似的，当它们的概率比，似然比，不依赖于网络中其他节点的实例。我们发现，状态的相似性暴露冗余的联合概率分布，可以用来减少计算时间的概率推理网络中的多个相似的状态，并在网络中的计算复杂性指数许多相似的状态可能是多项式。我们展示了我们的想法的例子BN 2 O网络-一个两层的网络经常用于诊断问题-通过减少它到一个非常接近的网络与多个类似的状态。我们表明，实际查询的答案收敛速度非常快，与原始网络获得的答案。对于只需要原始BN 2 O模型所需计算时间的10%的模型，最大误差低至5%。
英文摘要：
Although probabilistic inference in a general Bayesian belief network is an NP-hard problem, computation time for inference can be reduced in most practical cases by exploiting domain knowledge and by making approximations in the knowledge representation. In this paper we introduce the property of similarity of states and a new method for approximate knowledge representation and inference which is based on this property. We define two or more states of a node to be similar when the ratio of their probabilities, the likelihood ratio, does not depend on the instantiations of the other nodes in the network. We show that the similarity of states exposes redundancies in the joint probability distribution which can be exploited to reduce the computation time of probabilistic inference in networks with multiple similar states, and that the computational complexity in the networks with exponentially many similar states might be polynomial. We demonstrate our ideas on the example of a BN2O network -- a two layer network often used in diagnostic problems -- by reducing it to a very close network with multiple similar states. We show that the answers to practical queries converge very fast to the answers obtained with the original network. The maximum error is as low as 5% for models that require only 10% of the computation time needed by the original BN2O model.
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