Towards an algorithmic statistics

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1968, Issue , 2000, Pages 41-55

  Gács, Peter ^a   Tromp, John ^b   Vitáanyi, Paul ^b  

^a BOSTON UNIVERSITY   (United States)

^b CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY;

ALGORITHMIC STATISTICS; ALGORITHMIC THEORY; INDIVIDUAL MODELING; INDIVIDUAL OBJECTS; KOLMOGOROV COMPLEXITY; MEASURE OF INFORMATION; PROBABILISTIC ENSEMBLE; SUFFICIENT STATISTICS;

STATISTICS;

EID: 84974710146     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-40992-0_4     Document Type: Conference Paper

References (18)

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 and J.A. Thomas, Elements of Information Theory, Wiley, New York, 1991.
4. R. A. Fisher, On the mathematical foundations of theoretical statistics, Philosophical Transactions of the Royal Society of London, Ser. A, 222(1922), 309-368.
5. Q. Gao, M. Li and P.M.B. Vitànyi, Applying MDL to learn best model granularity, Artificial Intelligence, To appear. http://xxx.lanl.gov/abs/physics/0005062
6. P. Gàcs, J. Tromp, P. Vitànyi, Algorithmic statistics, Submitted. http://xxx.lanl.gov/abs/math.PR/0006233
7. M. Li and P.M.B. Vitànyi, An Introduction to Kolmogorov Complexity and its Applications, Springer-Verlag, New York, 2nd Edition, 1997.
8. A.N. Kolmogorov, Three approaches to the quantitative definition of information, Problems Inform. Transmission 1:1 (1965) 1-7.
9. A.N. Kolmogorov, On logical foundations of probability theory, Pp. 1-5 in: Probability Theory and Mathematical Statistics, Lect. Notes Math., Vol. 1021, K. Itô and Yu.V. Prokhorov, Eds., Springer-Verlag, Heidelberg, 1983.
10. A.N. Kolmogorov and V.A. Uspensky, Algorithms and Randomness, SIAM Theory Probab. Appl., 32:3(1988), 389-412.
11. L.A. Levin, Laws of information conservation (nongrowth) and aspects of the foundation of probability theory, Problems Inform. Transmission 10:3(1974), 206-210.
12. L.A. Levin Randomness conservation inequalities: information and independence in mathematical theories, Information and Control 61 (1984) 15-37.
13. P. Martin-Löf, The definition of random sequences, Inform. Contr., 9(1966), 602-619.
14. A.Kh. Shen, The concept of (α; β)-stochasticity in the Kolmogorov sense, and its properties, Soviet Math. Dokl., 28:1(1983), 295-299.
15. A.Kh. Shen, Discussion on Kolmogorov complexity and statistical analysis, The Computer Journal, 42:4(1999), 340-342.
16. P.M.B. Vitànyi and M. Li, Minimum Description Length Induction, Bayesianism, and Kolmogorov Complexity, IEEE Trans. Inform. Theory, IT-46:2(2000), 446-464.
17. 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., 32:3(1987), 508-512.
18. V.V. V'yugin, Algorithmic complexity and stochastic properties of finite binary sequences, The Computer Journal, 42:4(1999), 294-317.