Advertisement

Identification and Prediction

  • L. Bäumer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)

Abstract

In this work the concept of identification is applied in the theory of prediction. This approach was suggested to us by our advisor Professor R. Ahlswede. This and other directions of research can be found also in [2]. Well known is Shannon’s theory of transmission of messages over a noisy channel ([15]). Using the framework of Shannon’s channel model a new concept of information transfer – called identification – was introduced by Ahlswede and Dueck in [1].

Keywords

Prediction Rule Prediction Problem Comparison Class Sequential Predictor Human Opponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahlswede, R., Dueck, G.: Identification via channels. IEEE Trans. Inform. Theory 35(1), 15–29 (1989)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Ahlswede, R.: General theory of information transfer, Preprint 97–118, SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld (1997); General theory of information transfer:updated, General Theory of Information Transfer and Combinatorics, a Special Issue of Discrete Applied Mathematics (to appear)Google Scholar
  3. 3.
    Algoet, P.H.: The strong law of large numbers for sequential decisions under uncertainty. IEEE Trans. Inform. Theory 40(3), 609–633 (1994)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Blackwell, D.: An analog to the minimax theorem for vector payoffs. Pac. J. Math. 6, 1–8 (1956)MATHMathSciNetGoogle Scholar
  5. 5.
    Blackwell, D.: Controlled random walks. In: Proc. Int. Congr. Mathematicians, 1954, vol. III, pp. 336–338. North Holland, Amsterdam (1956)Google Scholar
  6. 6.
    Cover, T.M., Shenhar, A.: Compound Bayes predictors for sequences with apparent Markov structure. IEEE Trans. Syst. Man Cybern. SMC-7, 421–424 (1977)CrossRefGoogle Scholar
  7. 7.
    Cover, T.M.: Behavior of sequential predictors of binary sequences. In: Proc. 4th Prague Conf. Inform. Theory, Statistical Decision Functions, Random Processes, 1965, pp. 263–272. Publishing House of the Czechoslovak Academy of Sciences, Prague (1967)Google Scholar
  8. 8.
    Feder, M., Merhav, N., Gutman, M.: Universal prediction of individual sequences. IEEE Trans. Inform. Theory 38(4), 1258–1270 (1992)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Feder, M., Merhav, N., Gutman, M.: Some properties of sequential predictors for binary Markov sources. IEEE Trans. Inform. Theory 39(3), 887–892 (1993)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Feder, M., Merhav, N.: Universal schemes for sequential decision from individual data sequences. IEEE Trans. Inform. Theory 39(4), 1280–1292 (1993)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Feder, M., Merhav, N.: Relations between entropy and error probability. IEEE Trans. Inform. Theory 40(1), 259–266 (1994)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hannan, J.F., Robbins, H.: Asymptotic solutions of the compound decision problem for two completely specified distributions. Ann. Math. Statist. 26, 37–51 (1957)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Hannan, J.F.: Approximation to Bayes risk in repeated plays, Contributions to the Theory of Games. Annals of Mathematics Studies, vol. III, Princeton, NJ, No. 39, pp. 97–139 (1957)Google Scholar
  14. 14.
    Robbins, H.: Asymptotically subminimax solutions of compound statistical decision problems. In: Proc. 2nd Berkeley Symp. Math. Stat. Probab., pp. 131–148 (1951)Google Scholar
  15. 15.
    Shannon, C.E.: A mathematical theory of communication. Bell System Tech. J. 27, 379–423, 623–656 (1948)Google Scholar
  16. 16.
    Shannon, C.E.: Prediction and entropy of printed English. Bell Sys. Tech. J. 30, 5–64 (1951)Google Scholar
  17. 17.
    Shannon, C.E.: The mind reading machine. In: Wyner, A.D., Sloane, N.J.A. (eds.) Bell Laboratories Memorandum, 1953: Shannon’s Collected Papers, pp. 688–689. IEEE Press, Los Alamitos (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • L. Bäumer
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

Personalised recommendations