Asymptotic Log-loss of Prequential Maximum Likelihood Codes

Peter Grunwald; Steven de Rooij

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arXiv · cs/0502004

Asymptotic Log-loss of Prequential Maximum Likelihood Codes

Peter Grunwald·Steven de Rooij

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Abstract

We analyze the Dawid-Rissanen prequential maximum likelihood codes relative to one-parameter exponential family models M. If data are i.i.d. according to an (essentially) arbitrary P, then the redundancy grows at rate c/2 ln n. We show that c=v1/v2, where v1 is the variance of P, and v2 is the variance of the distribution m* in M that is closest to P in KL divergence. This shows that prequential codes behave quite differently from other important universal codes such as the 2-part MDL, Shtarkov and Bayes codes, for which c=1. This behavior is undesirable in an MDL model selection setting.

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BibTeX RIS

Peter Grunwald, Steven de Rooij. 2005-02-01. Asymptotic Log-loss of Prequential Maximum Likelihood Codes. https://arxiv.org/abs/cs/0502004

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