Research

Publications and preprints

1. N. Barnfield, R. Grondin, G. Pozzoli and R. Raquépas. On the Ziv-Merhav theorem beyond Markovianity II: A thermodynamic Approach.(2023). arXiv:2312.02098 [math.PR]
   • Abstract: 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. In particular, our results 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.
2. N. Barnfield, R. Grondin, G. Pozzoli and R. Raquépas. On the Ziv-Merhav theorem beyond Markovianity I. Canadian Journal of Mathematics. (2024). doi:10.4153/S0008414X24000178
   • Abstract: 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 Markov measures. The result covers pairs of suitably regular g-measures and pairs of equilibrium measures arising from the small space of interactions in mathematical statistical mechanics.

Conference proceedings

1. N. Barnfield, R. Grondin, G. Pozzoli and R. Raquépas. Ziv-Merhav estimation for hidden-Markov processes. IEEE International Symposium on Information Theory. (2024). doi:10.1109/ISIT57864.2024.10619304
   • 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.

Invited talks

Séminaire Doctorant (January 16, 2024)
Laboratoire de Mathématiques de Besançon, Besançon (online)
On the Ziv-Merhav theorem beyond Markovianity

The Seminars on Undergraduate Mathematics in Montreal (January 5, 2024)
Université du Québec à Montréal (UQÀM), Montréal
Entropic estimators in information theory

Mini-workshop on Entropies for Complex processes (December 9, 2023)
Mathematical institute of the Serbian Academy of Sciences and Arts, Belgrade (online)
Return times and waiting times as entropy estimators III: Ziv–Merhav Estimator

Recent Progress in Statistical Mechanics (December 3, 2023)
Winter Meeting of the Canadian Mathematical Society, Montréal
On the Ziv-Merhav theorem beyond Markovianity

Undergraduate Research Conference (August 18, 2022)
McGill University, Montréal
Estimating entropic quantities using recurrences and waiting times