Abstract
In this paper, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of regular conditional relative entropy between regular conditional probability measures is introduced as an a posteriori probability distance when a realized observation sequence is observed. Using a measure change and a relation between the Radon-Nikodym derivatives of probability measures and regular conditional probability measures, we derive a representation for regular conditional relative entropy. With this representation, we can calculate this distance using an information state approach. The regular conditional relative entropy rate is also considered.
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