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Algorithms 2012, 5(1), 50-55; doi:10.3390/a5010050

A Note on Sequence Prediction over Large Alphabets

Department of Computer Science and Engineering, Aalto University, 00076 Aalto, Finland
Received: 14 November 2011 / Revised: 11 February 2012 / Accepted: 13 February 2012 / Published: 17 February 2012
(This article belongs to the Special Issue Data Compression, Communication and Processing)
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Building on results from data compression, we prove nearly tight bounds on how well sequences of length n can be predicted in terms of the size σ of the alphabet and the length k of the context considered when making predictions. We compare the performance achievable by an adaptive predictor with no advance knowledge of the sequence, to the performance achievable by the optimal static predictor using a table listing the frequency of each (k + 1)-tuple in the sequence. We show that, if the elements of the sequence are chosen uniformly at random, then an adaptive predictor can compete in the expected case if k ≤ logσ n – 3 – ε, for a constant ε > 0, but not if k ≥ logσ n.
Keywords: sequence prediction; alphabet size; analysis sequence prediction; alphabet size; analysis
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Gagie, T. A Note on Sequence Prediction over Large Alphabets. Algorithms 2012, 5, 50-55.

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