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arXiv · 1712.02151

Generalized Probability Smoothing

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

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Christopher Mattern. 2017-12-06. Generalized Probability Smoothing. https://arxiv.org/abs/1712.02151

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