Convergence of discrete MDL for sequential prediction

Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)

Volumn 3120, Issue , 2004, Pages 300-314

  Poland, Jan ^a   Hutter, Marcus ^a  

^a DALLE MOLLE INSTITUTE FOR ARTIFICIAL INTELLIGENCE IDSIA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; ESTIMATION; LEARNING SYSTEMS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MIXTURES; RANDOM PROCESSES; THEOREM PROVING; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TURING MACHINES;

BAYES MIXTURES; MINIMUM DESCRIPTION LENGTH (MDL); RANDOMNESS; SEQUENCE PREDICTION; CONVERGENCE SPEED; CONVERGENCE THEOREM; MINIMUM DESCRIPTION LENGTH PRINCIPLE; SEQUENTIAL PREDICTION; UNIVERSAL INDUCTION; UNIVERSAL TURING MACHINE;

CONVERGENCE OF NUMERICAL METHODS; FORECASTING;

EID: 9444244517     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-27819-1_21     Document Type: Conference Paper

References (22)

1. Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Jrnl. 11 (1968) 185-194
2. Rissanen, J.J.: Modeling by shortest data description. Automatica 14 (1978) 465-471
3. Grünwald, P.D.: The Minimum Discription Length Principle and Reasoning under Uncertainty. PhD thesis, Universiteit van Amsterdam (1998)
4. Barron, A.R., Rissanen, J.J., Yu, B.: The minimum description length principle in coding and modeling. IEEE Transactions on Information Theory 44 (1998) 2743-2760
5. Rissanen, J.J.: Fisher Information and Stochastic Complexity. IEEE Trans on Information Theory 42 (1996) 40-47
6. Barron, A.R., Cover, T.M.: Minimum complexity density estimation. IEEE Transactions on Information Theory 37 (1991) 1034-1054
7. Rissanen, J.J.: Hypothesis selection and testing by the MDL principle. The Computer Journal 42 (1999) 260-269
8. Zvonkin, A.K., Levin, L.A.: The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. Russian Mathematical Surveys 25 (1970) 83-124
9. Li, M., Vitányi, P.M.B.: An introduction to Kolmogorov complexity and its applications. 2nd edn. Springer (1997)
10. Calude, C.S.: Information and Randomness. 2nd edn. Springer, Berlin (2002)
11. Solomonoff, R.J.: A formal theory of inductive inference: Part 1 and 2. Inform. Control 7 (1964) 1-22, 224-254
12. Solomonoff, R.J.: Complexity-based induction systems: comparisons and convergence theorems. IEEE Trans. Inform. Theory IT-24 (1978) 422-432
13. Hutter, M.: New error bounds for Solomonoff prediction. Journal of Computer and System Sciences 62 (2001) 653-667
14. Hutter, M.: Optimality of universal Bayesian prediction for general loss and alphabet. Journal of Machine Learning Research 4 (2003) 971-1000
15. Hutter, M.: Sequence prediction based on monotone complexity. In: Proceedings of the 16th Annual Conference on Learning Theory (COLT-2003). Lecture Notes in Artificial Intelligence, Berlin, Springer (2003) 506-521
16. Hutter, M.: Convergence and error bounds of universal prediction for general alphabet. Proceedings of the 12th Eurpean Conference on Machine Learning (ECML-2001) (2001) 239-250
17. Li, M., Chen, X., Li, X., Ma, B., Vitányi, P.M.B.: The similarity metric. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms (SODA). (2003)
18. Poland, J., Hutter, M.: On the convergence speed of MDL predictions for Bernoulli sequences, preprint (2004)
19. Gács, P.: On the relation between descriptional complexity and algorithmic probability. Theoretical Computer Science 22 (1983) 71-93
20. Levin, L.A.: On the notion of a random sequence. Soviet Math. Dokl. 14 (1973) 1413-1416
21. Schnorr, C.P.: Zufälligkeit und Wahrscheinlichkeit. Volume 218 of Lecture Notes in Mathematics. Springer, Chichester, England (1971)
22. Wang, Y.: Randomness and Complexity. PhD thesis, Ruprecht-Karls- Universität Heidelberg (1996)