Détail du document
Identifiant
oai:arXiv.org:2410.06589
Sujet
Computer Science - Information The... 94A12 (Primary), 94A29, 94A17 (Sec... H.1.1Auteur
Sagan, Naomi Weissman, TsachyCatégorie
Computer Science
Année
2024
Date de référencement
16/10/2024
Mots clés
family modelsRésumé
We propose and study a family of universal sequential probability assignments on individual sequences, based on the incremental parsing procedure of the Lempel-Ziv (LZ78) compression algorithm.
We show that the normalized log loss under any of these models converges to the normalized LZ78 codelength, uniformly over all individual sequences.
To establish the universality of these models, we consolidate a set of results from the literature relating finite-state compressibility to optimal log-loss under Markovian and finite-state models.
We also consider some theoretical and computational properties of these models when viewed as probabilistic sources.
Finally, we present experimental results showcasing the potential benefit of using this family -- as models and as sources -- for compression, generation, and classification.
;Comment: 31 pages, 5 figures, submitted to IEEE Transactions on Information Theory
Sagan, Naomi,Weissman, Tsachy, 2024, A Family of LZ78-based Universal Sequential Probability Assignments
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