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Complexity Monotone in Conditions and Future Prediction Errors

Authors: Alexey Chernov, Marcus Hutter, and Jürgen Schmidhuber

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract

We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor $M$ from the true distribution $mu$ by the algorithmic complexity of $mu$. Here we assume we are at a time $t>1$ and already observed $x=x_1...x_t$. We bound the future prediction performance on $x_{t+1}x_{t+2}...$ by a new variant of algorithmic complexity of $mu$ given $x$, plus the complexity of the randomness deficiency of $x$. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.

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Alexey Chernov, Marcus Hutter, and Jürgen Schmidhuber. Complexity Monotone in Conditions and Future Prediction Errors. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{chernov_et_al:DagSemProc.06051.6,
  author =	{Chernov, Alexey and Hutter, Marcus and Schmidhuber, J\"{u}rgen},
  title =	{{Complexity Monotone in Conditions and Future Prediction Errors}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--20},
  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/entities/document/10.4230/DagSemProc.06051.6},
  URN =		{urn:nbn:de:0030-drops-6327},
  doi =		{10.4230/DagSemProc.06051.6},
  annote =	{Keywords: Kolmogorov complexity, posterior bounds, online sequential prediction, Solomonoff prior, monotone conditional complexity, total error, future loss, ra}
}

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Complexity Monotone in Conditions and Future Prediction Errors

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