2024/10/09 by Naomi Sagan, Sagan, Naomi, Tsachy Weissman +1 · 1 citation
Computer Science · #94A12 (Primary) #94A17 (Secondary) #94A29 #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Computer and information sciences #H.1.1 #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2410.06589
openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.