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}
}
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Keywords: |
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Sequence prediction, Solomonoff induction, enumerable semimeasures |
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Collection: |
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06051 - Kolmogorov Complexity and Applications |
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Issue Date: |
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2006 |
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Date of publication: |
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31.07.2006 |
Creative Commons Attribution 4.0 International license (CC BY 4.0)