Abstract
We combine Solomonoff’s approach to universal prediction with algorithmic statistics and suggest to use the computable measure that provides the best “explanation” for the observed data (in the sense of algorithmic statistics) for prediction. In this way we keep the expected sum of squares of prediction errors bounded (as it was for the Solomonoff’s predictor) and, moreover, guarantee that the sum of squares of prediction errors is bounded along any Martin-Löf random sequence.
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Notes
- 1.
One may even require that the probabilities for finite outputs, i.e., the differences \(S(x)-S(x0)-S(x1)\) are maximal, but we do not require this.
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Acknowledgements
I would like to thank Alexander Shen and Nikolay Vereshchagin and for useful discussions, advice and remarks. This work is supported by 19-01-00563 RFBR grant and by RaCAF ANR-15-CE40-0016-01 grant.
The article was prepared within the framework of the HSE University Basic Research Program.
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Milovanov, A. (2021). Predictions and Algorithmic Statistics for Infinite Sequences. In: Santhanam, R., Musatov, D. (eds) Computer Science – Theory and Applications. CSR 2021. Lecture Notes in Computer Science(), vol 12730. Springer, Cham. https://doi.org/10.1007/978-3-030-79416-3_17
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