Complexity Monotone in Conditions and Future Prediction Errors

2006/01/01 by Alexey Chernov, Chernov, Alexey, Marcus Hütter +3
Computer Science · Mathematics · #Algorithms and Data Compression #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #Kolmogorov complexity #Solomonoff prior #future loss #monotone conditional complexity #online sequential prediction #posterior bounds #ra #total error

paper · doi:10.4230/dagsemproc.06051.6

openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=x₁...x_t. We bound the future prediction performance on x_t+1x_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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