A Family of LZ78-based Universal Sequential Probability Assignments

Document detail

ID

oai:arXiv.org:2410.06589

Topic

Computer Science - Information The... 94A12 (Primary), 94A29, 94A17 (Sec... H.1.1

Author

Sagan, Naomi Weissman, Tsachy

Year

2024

listing date

10/16/2024

Keywords

family models

Metrics

Abstract

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