Prediction of Large Alphabet Processes and Its Application to Adaptive Source Coding
Boris Ryabko, Jaakko Astola
Abstract
The problem of predicting a sequence x1,x2,... generated by a discrete source with unknown statistics is considered. Each letter xt+1 is predicted using information on the word x1x2... xt 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 xi 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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