### Abstract

Language | English |
---|---|

Pages | 242-261 |

Number of pages | 20 |

Journal | Information And Computation |

Volume | 205 |

Issue number | 2 |

DOIs | |

State | Published - 28 Feb 2007 |

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### Bibliographical note

© 2007. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/### Keywords

- Kolmogorov complexity
- posterior bounds
- online sequential prediction
- Solomonoff prior
- monotone conditional complexity
- total error
- future loss
- randomness deficiency

### Cite this

*205*(2), 242-261. DOI: 10.1016/j.ic.2006.10.004

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**Algorithmic complexity bounds on future prediction errors.** / Chernov, Alexey; Hutter, Marcus; Schmidhuber, Juergen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Algorithmic complexity bounds on future prediction errors

AU - Chernov,Alexey

AU - Hutter,Marcus

AU - Schmidhuber,Juergen

N1 - © 2007. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

PY - 2007/2/28

Y1 - 2007/2/28

N2 - 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 μ by the algorithmic complexity of μ . Here we assume that we are at a time t>1 and have already observed x = x 1...xt . We bound the future prediction performance on xt+1xt+2... by a new variant of algorithmic complexity of μ 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.

AB - 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 μ by the algorithmic complexity of μ . Here we assume that we are at a time t>1 and have already observed x = x 1...xt . We bound the future prediction performance on xt+1xt+2... by a new variant of algorithmic complexity of μ 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.

KW - Kolmogorov complexity

KW - posterior bounds

KW - online sequential prediction

KW - Solomonoff prior

KW - monotone conditional complexity

KW - total error

KW - future loss

KW - randomness deficiency

U2 - 10.1016/j.ic.2006.10.004

DO - 10.1016/j.ic.2006.10.004

M3 - Article

VL - 205

SP - 242

EP - 261

IS - 2

ER -