On Probability Estimation by Exponential Smoothing

Christopher Mattern

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arXiv · 1501.01202

On Probability Estimation by Exponential Smoothing

Christopher Mattern

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Abstract

Probability estimation is essential for every statistical data compression algorithm. In practice probability estimation should be adaptive, recent observations should receive a higher weight than older observations. We present a probability estimation method based on exponential smoothing that satisfies this requirement and runs in constant time per letter. Our main contribution is a theoretical analysis in case of a binary alphabet for various smoothing rate sequences: We show that the redundancy w.r.t. a piecewise stationary model with $s$ segments is $O\left(s\sqrt n\right)$ for any bit sequence of length $n$, an improvement over redundancy $O\left(s\sqrt{n\log n}\right)$ of previous approaches with similar time complexity.

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Christopher Mattern. 2015-01-06. On Probability Estimation by Exponential Smoothing. https://arxiv.org/abs/1501.01202

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