  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.
