Exact Computation of Kullback-Leibler Distance for Hidden Markov Trees and Models

Details Exact Computation of Kullback-Leibler Distance for Hidden Markov Trees and Models Exact Computation of Kullback-Leibler Distance for Hidden Markov Trees and Models

2011-12-14

arxiv.org/abs/1112.3257v1

Computer Science

Information Theory

Scientific paper

We suggest new recursive formulas to compute the exact value of the Kullback-Leibler distance (KLD) between two general Hidden Markov Trees (HMTs). For homogeneous HMTs with regular topology, such as homogeneous Hidden Markov Models (HMMs), we obtain a closed-form expression for the KLD when no evidence is given. We generalize our recursive formulas to the case of HMMs conditioned on the observable variables. Our proposed formulas are validated through several numerical examples in which we compare the exact KLD value with Monte Carlo estimations.

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