广义概率平滑

摘要：

在这项工作中，我们考虑一个广义版本的概率平滑，核心基本模型的顺序预测的最先进的PAQ家庭的数据压缩算法。我们的主要贡献是一个码长分析，认为冗余的概率平滑相对于分段平稳源。该分析适用于一个有限的字母表，并表示冗余的分段平稳源的平稳分布的概率质量的总变化。通过适当地选择参数，概率平滑对于长度为$T$的序列相对于具有$S$段的分段平稳源具有冗余$O(S\cdot\sqrt{T\log T})$。

英文摘要：

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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