DagSemProc.06051.7.pdf
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Error in Enumerable Sequence Prediction
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Dagstuhl Seminar Proceedings, Volume 6051
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2006-07-31
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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
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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