An Open Problem Regarding the Convergence of Universal A Priori Probability

  • Marcus Hutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2777)

Abstract

Is the textbook result that Solomonoff’s universal posterior converges to the true posterior for all Martin-Löf random sequences true?

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hutter, M.: On the existence and convergence of computable universal priors. Technical Report IDSIA-05-03 (2003), http://arxiv.org/abs/cs.LG/0305052
  2. 2.
    Levin, L.A.: On the notion of a random sequence. Soviet Math. Dokl. 14(5), 1413–1416 (1973)MATHGoogle Scholar
  3. 3.
    Li, M., Vitányi, P.M.B.: An introduction to Kolmogorov complexity and its applications, 2nd edn. Springer, Heidelberg (1997)Google Scholar
  4. 4.
    Solomonoff, R.J.: A formal theory of inductive inference: Part 1 and 2. Inform. Control 7, 1-22, 224–254 (1964)Google Scholar
  5. 5.
    Solomonoff, R.J.: Complexity-based induction systems: comparisons and convergence theorems. IEEE Trans. Inform. Theory IT-24, 422–432 (1978)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Vitányi, P.M.B., Li, M.: Minimum description length induction, Bayesianism, and Kolmogorov complexity. IEEE Transactions on Information Theory 46(2), 446–464 (2000)MATHCrossRefGoogle Scholar
  7. 7.
    Vovk, V.G.: On a randomness criterion. Soviet Mathematics Doklady 35(3), 656–660 (1987)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Marcus Hutter
    • 1
  1. 1.IDSIAManno-LuganoSwitzerland

Personalised recommendations