Learning with side information: PAC learning bounds

Journal of Computer and System Sciences

Volumn 68, Issue 3, 2004, Pages 521-545

  Kuusela, P ^a,b   Ocone, D ^a  

^a RUTGERS UNIVERSITY   (United States)

^b AALTO UNIVERSITY   (Finland)

Author keywords

Dependent data; Learning theory; Probably Approximately Correct learning; Uniform convergence of empirical means

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DATA REDUCTION; INFORMATION ANALYSIS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; QUADRATIC PROGRAMMING; SET THEORY;

DEPENDENT DATA; LEARNING THEORY; PROBABLY APPROXIMATELY CORRECT LEARNING; UNIFORM CONVERGENCE OF EMPIRICAL MEANS;

LEARNING SYSTEMS;

EID: 2342559143     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcss.2003.07.005     Document Type: Article

References (21)

1. Y. Abu-Mostafa, Hints and the VC dimension, Neural Comput. 5 (1993) 278-288.
2. Y. Abu-Mostafa, Learning from hints, J. Complexity 10 (1994) 165-178.
3. Y. Abu-Mostafa, Hints, Neural Comput. 7 (1995) 639-671.
4. A. Blum, T. Mitchell, Combining labeled and unlabeled data with co-training, in: Proceedings of the 11th Annual Conference on Computational Learning Theory, 1998, pp. 92-100.
5. M. Campi, P. Kumar, Leaning dynamical systems in a stationary environment, Syst. Control Lett. 34 (3) (1998) 125-132.
6. C. Dellacherie, P.-A. Meyer, Probabilities and Potential, North-Holland, Amsterdam, 1978.
7. A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Applications of Mathematics, Vol. 38, 2nd Edition, Springer, Berlin, 1998.
8. L. Devroye, Bounds for the uniform deviation of empirical measures, J. Multivariate Anal. 12 (1982) 72-79.
9. W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963) 13-30.
10. V. Koltchinskii, C. Abdullah, M. Ariola, P. Dorato, D. Panchenko, Improved sample complexity estimates for statistical learning control of uncertain systems, IEEE Trans. Automat. Control 45 (12) (2000) 2383-2388.
11. P. Kuusela, Learning theory techniques in control theory, Ph.D. Thesis, Department of Mathematics, Rutgers, the State University of New Jersey, available from www.math.rutgers.edu/kuusela 1999.
12. P. Kuusela, D. Ocone, Learning with side information: an example, 2001, submitted for publication.
13. R. Meir, Performance bounds for nonlinear time series prediction, in: Proceedings of the Tenth Annual Conference on Computational Learning Theory, Nashville, Tennessee, 1997.
14. D. Pollard, Convergence of Stochastic Processes, Springer Series in Statistics, Springer, Berlin, 1984.
15. J. Ratsaby, V. Maiorov, On the value of partial information for learning from examples, J. Complexity 13 (4) (1997) 509-544.
16. J. Shawe-Taylor, M. Anthony, N.L. Biggs, Bounding sample size with the Vapnik-Chervonenkis dimension, Discrete Appl. Math. 42 (1993) 65-73.
17. V. Vapnik, A. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities, J. Probab. Appl. 16 (1971) 264-280.
18. N. Vayatis, Inégalités de Vapnik-Chervonenkis et measures de complexité, Ph.D. Thesis, Ecole Polytechnique (in English), available from www./www.cmla.ens-cachan.fr/Utilisateurs/vayatis/2000.
19. N. Vayatis, The role of critical sets in Vapnik-Chervonenkis theory, in: Proceedings of COLT, Palo Alto, California, 2000, pp. 75-80.
20. N. Vayatis, R. Azencott, Distribution dependent Vapnik-Chervonenkis bounds, Computational Learning Theory, Lecture Notes in Artificial Intelligence, Vol. 1572, 1999, pp. 230-240.
21. M. Vidyasagar, A Theory of Learning and Generalization; With Applications to Neural Networks and Control Systems, Springer, Berlin, 1997.