Error in Enumerable Sequence Prediction

Author Nick Hay



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Nick Hay

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Nick Hay. Error in Enumerable Sequence Prediction. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)
https://doi.org/10.4230/DagSemProc.06051.7

Abstract

We outline a method for quantifying the error of a sequence prediction. With sequence predictions represented by semimeasures $ u(x)$ we define their error to be $-log_2 u(x)$. We note that enumerable semimeasures are those which model the sequence as the output of a computable system given unknown input. Using this we define the simulation complexity of a computable system $C$ relative to another $U$ giving an emph{exact} bound on their difference in error. This error in turn gives an exact upper bound on the number of predictions $ u$ gets incorrect.
Keywords
  • Sequence prediction
  • Solomonoff induction
  • enumerable semimeasures

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