- Approximation of the I-divergence between stationary and hidden Markov processes
- 2008 International Workshop on Applied Probability (IWAP 2008), Compiègne, France
- Book/source title
- Proceedings of the 2008 International Workshop on Applied Probability (IWAP 2008)
- Compiègne, France: Université de Technologie de Compiègne
- Document type
- Conference contribution
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
We aim at the construction of a Hidden Markov Model (HMM) of assigned complexity (number of states of the underlying Markov chain) which best approximates, in Kullback-Leibler divergence rate, a given stationary process. We establish, under mild conditions, the existence of the divergence rate between a stationary process and an HMM. Since in general there is no analytic expression available for this divergence rate, we approximate it with a properly defined, and easily computable, divergence between Hankel matrices, which we propose as an approximation criterion.
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