Computational complexity reduction for BN2O networks using similarity of states

Although probabilistic inference in a general Bayesian belief network is an NP-hard prob­ lem, computation time for inference can be reduced in most practical cases by exploiting domain knowledge and by making approxi­ mations in the knowledge representation. In this paper we introduce the property of sim­ ilarity of states and a new method for ap­ proximate knowledge representation and in­ ference 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 net­ work. 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 infer­ ence in networks with multiple similar states, and that the comput.at.ional complexity in the networks with exponent,ially many sim­ ilar states might be polynomial. We demon­ strate our ideas on the example of a BN20 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 lhe original network. The maximum er­ ror is as low as 5% for models that require only 10% of the computation time needed by the original BN20 model.