Geodesic
On the Ziv–Merhav theorem beyond Markovianity I
Canadian journal of mathematics, Tome 77 (2025) no. 3, pp. 891-915

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DOI

We generalize to a broader class of decoupled measures a result of Ziv and Merhav on universal estimation of the specific cross (or relative) entropy, originally for a pair of multilevel Markov measures. Our generalization focuses on abstract decoupling conditions and covers pairs of suitably regular g-measures and pairs of equilibrium measures arising from the “small space of interactions” in mathematical statistical mechanics.
DOI : 10.4153/S0008414X24000178
Mots-clés : Cross entropy, estimator, parsing, match lengths, decoupling 
Barnfield, Nicholas; Grondin, Raphaël; Pozzoli, Gaia; Raquépas, Renaud. On the Ziv–Merhav theorem beyond Markovianity I. Canadian journal of mathematics, Tome 77 (2025) no. 3, pp. 891-915. doi: 10.4153/S0008414X24000178
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     title = {On the {Ziv{\textendash}Merhav} theorem beyond {Markovianity} {I}},
     journal = {Canadian journal of mathematics},
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     year = {2025},
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