Computer Science > Information Theory
[Submitted on 25 Feb 2022 (v1), last revised 1 May 2024 (this version, v3)]
Title:Alpha-NML Universal Predictors
View PDF HTML (experimental)Abstract:Inspired by the connection between classical regret measures employed in universal prediction and Rényi divergence, we introduce a new class of universal predictors that depend on a real parameter $\alpha\geq 1$. This class interpolates two well-known predictors, the mixture estimators, that include the Laplace and the Krichevsky-Trofimov predictors, and the Normalized Maximum Likelihood (NML) estimator. We point out some advantages of this new class of predictors and study its benefits from two complementary viewpoints: (1) we prove its optimality when the maximal Rényi divergence is considered as a regret measure, which can be interpreted operationally as a middle ground between the standard average and worst-case regret measures; (2) we discuss how it can be employed when NML is not a viable option, as an alternative to other predictors such as Luckiness NML. Finally, we apply the $\alpha$-NML predictor to the class of discrete memoryless sources (DMS), where we derive simple formulas to compute the predictor and analyze its asymptotic performance in terms of worst-case regret.
Submission history
From: Marco Bondaschi [view email][v1] Fri, 25 Feb 2022 14:55:18 UTC (30 KB)
[v2] Wed, 4 Jan 2023 22:08:48 UTC (34 KB)
[v3] Wed, 1 May 2024 15:33:55 UTC (34 KB)
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