4 papers
Stability of the Shannon--McMillan--Breiman Theorem under Sublinear Parsings
Raphael Grondin
We establish a stability result for the Shannon-McMillan-Breiman theorem on the one-sided finite shift space. For any shift-invariant probability measure P and any data-dependent p…
Ziv-Merhav estimation for hidden-Markov processes
Nicholas Barnfield, Raphaël Grondin, Gaia Pozzoli +1
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: th…
On the Ziv-Merhav theorem beyond Markovianity II: leveraging the thermodynamic formalism
Nicholas Barnfield, Raphaël Grondin, Gaia Pozzoli +1
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 g…
On the Ziv-Merhav theorem beyond Markovianity
Nicholas Barnfield, Raphaël Grondin, Gaia Pozzoli +1
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 for a pair of multi-level Mark…