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

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

2005-04-17

arxiv.org/abs/cs/0504079v2

Computer Science

Information Theory

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Scientific paper

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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