On the Ziv-Merhav theorem beyond Markovianity II: leveraging the thermodynamic formalism
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910380880560128 |
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| author | Barnfield, Nicholas Grondin, Raphaël Pozzoli, Gaia Raquépas, Renaud |
| author_facet | Barnfield, Nicholas Grondin, Raphaël Pozzoli, Gaia Raquépas, Renaud |
| contents | We prove asymptotic results for a modification of the cross-entropy estimator originally introduced by Ziv and Merhav in the Markovian setting in 1993. Our results concern a more general class of decoupled measures on shift spaces over a finite alphabet and in particular imply strong asymptotic consistency of the modified estimator for all pairs of functions of stationary, irreducible, finite-state Markov chains satisfying a mild decay condition. Our approach is based on the study of a rescaled cumulant-generating function called the cross-entropic pressure, importing to information theory some techniques from the study of large deviations within the thermodynamic formalism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_02098 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Ziv-Merhav theorem beyond Markovianity II: leveraging the thermodynamic formalism Barnfield, Nicholas Grondin, Raphaël Pozzoli, Gaia Raquépas, Renaud Probability Information Theory Dynamical Systems 94A17, 37M25, 60F15, 37D35 We prove asymptotic results for a modification of the cross-entropy estimator originally introduced by Ziv and Merhav in the Markovian setting in 1993. Our results concern a more general class of decoupled measures on shift spaces over a finite alphabet and in particular imply strong asymptotic consistency of the modified estimator for all pairs of functions of stationary, irreducible, finite-state Markov chains satisfying a mild decay condition. Our approach is based on the study of a rescaled cumulant-generating function called the cross-entropic pressure, importing to information theory some techniques from the study of large deviations within the thermodynamic formalism. |
| title | On the Ziv-Merhav theorem beyond Markovianity II: leveraging the thermodynamic formalism |
| topic | Probability Information Theory Dynamical Systems 94A17, 37M25, 60F15, 37D35 |
| url | https://arxiv.org/abs/2312.02098 |