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arXiv · 1002.0757

Prequential Plug-In Codes that Achieve Optimal Redundancy Rates even if the Model is Wrong

Peter Grünwald·Wojciech Kotłowski
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Abstract

We analyse the prequential plug-in codes relative to one-parameter exponential families M. We show that if data are sampled i.i.d. from some distribution outside M, then the redundancy of any plug-in prequential code grows at rate larger than 1/2 ln(n) in the worst case. This means that plug-in codes, such as the Rissanen-Dawid ML code, may behave inferior to other important universal codes such as the 2-part MDL, Shtarkov and Bayes codes, for which the redundancy is always 1/2 ln(n) + O(1). However, we also show that a slight modification of the ML plug-in code, "almost" in the model, does achieve the optimal redundancy even if the the true distribution is outside M.

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Peter Grünwald, Wojciech Kotłowski. 2010-02-03. Prequential Plug-In Codes that Achieve Optimal Redundancy Rates even if the Model is Wrong. https://arxiv.org/abs/1002.0757

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