English

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 O(STlogT)O(S\cdot\sqrt{T\log T}) for sequences of length TT with respect to a Piecewise Stationary Source with SS segments.

Keywords

Cite

@article{arxiv.1712.02151,
  title  = {Generalized Probability Smoothing},
  author = {Christopher Mattern},
  journal= {arXiv preprint arXiv:1712.02151},
  year   = {2018}
}