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arXiv · 1401.3760

Large Alphabet Compression and Predictive Distributions through Poissonization and Tilting

Xiao Yang·Andrew R. Barron
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Abstract

This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size $m$. In particular, the size of the sample is allowed to be variable. The employment of a Poisson model and tilting method simplifies the implementation and analysis through independence. The resulting strategy is optimal within the class of distributions satisfying a moment condition, and is close to optimal for the class of all i.i.d distributions on strings of a given length. Moreover, the method can be used to code and predict strings with a condition on the tail of the ordered counts. It can also be applied to distributions in an envelope class.

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Xiao Yang, Andrew R. Barron. 2014-01-15. Large Alphabet Compression and Predictive Distributions through Poissonization and Tilting. https://arxiv.org/abs/1401.3760

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