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URN: urn:nbn:de:0030-drops-6331

Error in Enumerable Sequence Prediction



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.

BibTeX - Entry

  author =	{Nick Hay},
  title =	{Error in Enumerable Sequence Prediction},
  booktitle =	{Kolmogorov Complexity and Applications},
  year =	{2006},
  editor =	{Marcus Hutter  and Wolfgang Merkle and Paul M.B. Vitanyi},
  number =	{06051},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Sequence prediction, Solomonoff induction, enumerable semimeasures}

Keywords: Sequence prediction, Solomonoff induction, enumerable semimeasures
Seminar: 06051 - Kolmogorov Complexity and Applications
Issue date: 2006
Date of publication: 31.07.2006

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