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Prediction of Large Alphabet Processes and Its Application to Adaptive Source Coding

Boris Ryabko·Jaakko Astola
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Abstract

The problem of predicting a sequence $x_1,x_2,...$ generated by a discrete source with unknown statistics is considered. Each letter $x_{t+1}$ is predicted using information on the word $x_1x_2... x_t$ only. In fact, this problem is a classical problem which has received much attention. Its history can be traced back to Laplace. We address the problem where each $x_i$ belongs to some large (or even infinite) alphabet. A method is presented for which the precision is greater than for known algorithms, where precision is estimated by the Kullback-Leibler divergence. The results can readily be translated to results about adaptive coding.

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Boris Ryabko, Jaakko Astola. 2005-04-21. Prediction of Large Alphabet Processes and Its Application to Adaptive Source Coding. https://arxiv.org/abs/cs/0504079

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