On the Foundations of Universal Sequence Prediction
<|reference_start|>On the Foundations of Universal Sequence Prediction: Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. We show that Solomonoff's model possesses many desirable properties: Fast convergence and strong bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well (actually better) in non-computable environments.<|reference_end|>
@article{hutter2006on,
    title={On the Foundations of Universal Sequence Prediction},
    author={Marcus Hutter},
    journal={Proc. 3rd Annual Conference on Theory and Applications of Models
  of Computation (TAMC 2006) pages 408-420},
    year={2006},
    number={IDSIA-03-06},
    archivePrefix={arXiv},
    eprint={cs/0605009},
    primaryClass={cs.LG cs.IT math.IT math.ST stat.TH}
}