Generalized Probability Smoothing
Information Theory
2018-01-11 v2 math.IT
Abstract
In this work we consider a generalized version of Probability Smoothing, the core elementary model for sequential prediction in the state of the art PAQ family of data compression algorithms. Our main contribution is a code length analysis that considers the redundancy of Probability Smoothing with respect to a Piecewise Stationary Source. The analysis holds for a finite alphabet and expresses redundancy in terms of the total variation in probability mass of the stationary distributions of a Piecewise Stationary Source. By choosing parameters appropriately Probability Smoothing has redundancy for sequences of length with respect to a Piecewise Stationary Source with segments.
Cite
@article{arxiv.1712.02151,
title = {Generalized Probability Smoothing},
author = {Christopher Mattern},
journal= {arXiv preprint arXiv:1712.02151},
year = {2018}
}