Large Alphabet Compression and Predictive Distributions through Poissonization and Tilting
Information Theory
2014-01-17 v1 math.IT
Methodology
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 . 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.
Cite
@article{arxiv.1401.3760,
title = {Large Alphabet Compression and Predictive Distributions through Poissonization and Tilting},
author = {Xiao Yang and Andrew R. Barron},
journal= {arXiv preprint arXiv:1401.3760},
year = {2014}
}