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DOI: 10.4230/DagSemProc.06051.7
URN: urn:nbn:de:0030-drops-6331
URL: https://drops.dagstuhl.de/opus/volltexte/2006/633/
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Hay, Nick

Error in Enumerable Sequence Prediction

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06051.HayNick.ExtAbstract.633.pdf (0.1 MB)


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.

BibTeX - Entry

@InProceedings{hay:DagSemProc.06051.7,
  author =	{Hay, Nick},
  title =	{{Error in Enumerable Sequence Prediction}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2006/633},
  URN =		{urn:nbn:de:0030-drops-6331},
  doi =		{10.4230/DagSemProc.06051.7},
  annote =	{Keywords: Sequence prediction, Solomonoff induction, enumerable semimeasures}
}

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


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