Kolmogorov's structure functions with an application to the foundations of model selection

Annual Symposium on Foundations of Computer Science - Proceedings

Volumn , Issue , 2002, Pages 751-760

  Vereshchagin, Nikolai ^a   Vitányi, Paul ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; FUNCTION EVALUATION; MATHEMATICAL MODELS; MAXIMUM PRINCIPLE; RANDOM PROCESSES; STATISTICAL METHODS;

ALGORITHMIC SUFFICIENT STATISTIC; DATA TO MODEL CODE LENGTH; KOLMOGOROV STRUCTURE FUNCTIONS; MAXIMAL COMPLEXITY;

COMPUTER SCIENCE;

EID: 0036954331     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (27)

1. A.R. Barron, J. Rissanen, and B. Yu, The minimum description length principle in coding and modeling, IEEE Trans. Inform. Theory, IT-44:6 (1998), 2743-2760.
2. T.M. Cover, Kolmogorov complexity, data compression, and inference, pp. 23-33 in The Impact of Processing Techniques on Communications, J. K. Skwirzynski, Ed., Martinus Nijhoff Publishers, 1985.
3. T.M. Cover, Attending [15]. Email to PV, January 24, 2002.
4. T.M. Cover, P. Gács and R.M. Gray, Kolmogorov's contributions to Information Theory and Algorithmic Complexity, Ann. Probab., 17 (1989), 840-865.
5. T.M. Cover and J.A. Thomas, Elements of Information Theory; Wiley, New York, 1991.
6. R.A. Fisher, On the mathematical foundations of theoretical statistics, Philosophical Transactions of the Royal Society of London, Ser. A, 222 (1922), 309-368.
7. P. Gács, On the symmetry of algorithmic information, Soviet Math. Dokl., 15 (1974) 1477-1480.
8. P. Ǵcs, Correction: ibid., 15 (1974) 1480.
9. P. Gács, Attending [15], Email to PV, January 24, 2002.
10. P. Gács, J. Tromp, P.M.B. Vitányi. Algorithmic statistics, IEEE Trans. Inform. Theory, 47:6(2001), 2443-2463.
11. Q. Gao, M. Li and P.M.B. Vitányi, Applying MDL to learn best model granularity, Artificial Intelligence, 121 (2000), 1-29.
12. L.A. Levin, Emails to PV on February 7,11,20, 2002.
13. M. Li and P.M.B. Vitányi, An Introduction to Kolmogorov Complexity and its Applications, Springer-Verlag, New York, 2nd Edition, 1997.
14. A.N. Kolmogorov, Three approaches to the quantitative definition of information, Problems Inform. Transmission 1:1 (1965) 1-7.
15. A.N. Kolmogorov, Complexity of Algorithms and Objective Definition of Randomness. A talk at Moscow Math. Soc. meeting 4/16/1974. An abstract available in Uspekhi Mat. Nauk 29:4 (1974), 155; translation in Section 5.
16. A. N. Kolmogorov. Talk at the Information Theory Symposium in Tallinn, Estonia, 1974. according to [8, 3].
17. P. Martin-Löf, The definition of random sequences. Inform. Contr., 9(1966), 602-619.
18. J.J. Rissanen, A Universal Prior for Integers and Estimation by Minimum Description Length, Annals of Statistics, 11:2 (1983), 416-431.
19. A. Kh. Shen, The concept of (α, β)-stochasticity in the Kolmogorov sense, and its properties. Soviet Math. Dokl., 28:1 (1983), 295-299.
20. A. Kh. Shen, Discussion on Kolmogorov complexity and statistical analysis. The Computer Journal, 42:4 (1999), 340-342.
21. P.M.B. Vitányi and M. Li, Minimum Description Length Induction, Bayesianism, and Kolmogorov Complexity, IEEE Trans. Inform. Theory, IT-46:2 (2000), 446-464.
22. P.M.B. Vitányi, Meaningful information, Proc. ISAAC 2002, LNCS, Springer-Verlag, Berlin, 2002. http://xxx.lanl.gov/abs/cs.CC/0111053
23. V.V. V'yugin, On the defect of randomness of a finite object with respect to measures with given complexity bounds, SIAM Theory Probab. Appl., 32:32 (1987), 508-512.
24. V.V. V'yugin, Algorithmic complexity and stochastic properties of finite binary sequences, The Computer Journal, 42:4 (1999), 294-317.
25. V.V. V'yugin, Does snooping help? Theoret. Comput. Sci., 276:1/2 (2002), 407-415.
26. C.S. Wallace and P. R. Freeman, Estimation and inference by compact coding, J. Royal Stat. Soc., Series B, 49, (1987) 240-251
27. C. S. Wallace and P. R. Freeman, Estimation and inference by compact coding, Discussion: ibid., 252-265.