Prequential Plug-In Codes that Achieve Optimal Redundancy Rates even if the Model is Wrong
Information Theory
2010-02-04 v1 Machine Learning
math.IT
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1002.0757,
title = {Prequential Plug-In Codes that Achieve Optimal Redundancy Rates even if the Model is Wrong},
author = {Peter Grünwald and Wojciech Kotłowski},
journal= {arXiv preprint arXiv:1002.0757},
year = {2010}
}