We present a proof of strong consistency of a Ziv-Merhav-type estimator of the cross entropy rate for pairs of hidden-Markov processes. Our proof strategy has two novel aspects: the focus on decoupling properties of the laws and the use of tools from the thermodynamic formalism.
Barnfield, N., Grondin, R., Pozzoli, G., Raquépas, R. (2024). Ziv-Merhav Estimation for Hidden-Markov Processes. In 2024 IEEE International Symposium on Information Theory (ISIT) (pp.3606-3611). IEEE [10.1109/isit57864.2024.10619304].
Ziv-Merhav Estimation for Hidden-Markov Processes
Pozzoli, Gaia;
2024
Abstract
We present a proof of strong consistency of a Ziv-Merhav-type estimator of the cross entropy rate for pairs of hidden-Markov processes. Our proof strategy has two novel aspects: the focus on decoupling properties of the laws and the use of tools from the thermodynamic formalism.
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