# Algorithmic complexity bounds on future prediction errors

Alexey Chernov, Marcus Hutter, Juergen Schmidhuber

Research output: Contribution to journalArticleResearchpeer-review

### 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 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.
Original language English 242-261 20 Information And Computation 205 2 10.1016/j.ic.2006.10.004 Published - 28 Feb 2007

### Fingerprint

Algorithmic Complexity
Prediction Error
Performance Prediction
Bayesian Model
Classification Problems
Randomness
Predictors
Monotone
Deviation
Decrease

### Keywords

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

### Cite this

Chernov, Alexey ; Hutter, Marcus ; Schmidhuber, Juergen. / Algorithmic complexity bounds on future prediction errors. 2007 ; Vol. 205, No. 2. pp. 242-261.
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Algorithmic complexity bounds on future prediction errors. / Chernov, Alexey; Hutter, Marcus; Schmidhuber, Juergen.

Vol. 205, No. 2, 28.02.2007, p. 242-261.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Hutter, Marcus

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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

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