No CrossRef data available.
Article contents
PAC Learning under Helpful Distributions
Published online by Cambridge University Press: 15 April 2002
Abstract
A PAC teaching model -under helpful distributions -is proposed which introduces the classical ideas of teaching models within the PAC setting: a polynomial-sized teaching set is associated with each target concept; the criterion of success is PAC identification; an additional parameter, namely the inverse of the minimum probability assigned to any example in the teaching set, is associated with each distribution; the learning algorithm running time takes this new parameter into account. An Occam razor theorem and its converse are proved. Some classical classes of boolean functions, such as Decision Lists, DNF and CNF formulas are proved learnable in this model. Comparisons with other teaching models are made: learnability in the Goldman and Mathias model implies PAC learnability under helpful distributions. Note that Decision lists and DNF are not known to be learnable in the Goldman and Mathias model. A new simple PAC model, where "simple" refers to Kolmogorov complexity, is introduced. We show that most learnability results obtained within previously defined simple PAC models can be simply derived from more general results in our model.
- Type
- Research Article
- Information
- Copyright
- © EDP Sciences, 2001
References
Angluin, D., Learning Regular Sets from Queries and Counterexamples.
Inform. and Comput.
75 (1987) 87-106.
CrossRef
Angluin, D., Queries and Concept Learning.
Machine Learning
2 (1988) 319-342.
G.M. Benedek and A. Itai, Nonuniform Learnability, in ICALP (1988) 82-92.
Blumer, A., Ehrenfeucht, A., Haussler, D. and Warmuth, M.K., Occam's Razor.
Inform. Process. Lett.
24 (1987) 377-380.
CrossRef
Board, R. and Pitt, L., On the Necessity of Occam Algorithms.
Theoret. Comput. Sci.
100 (1992) 157-184.
CrossRef
Bshouty, N.H., Exact Learning Boolean Function via the Monotone Theory.
Inform. and Comput.
123 (1995) 146-153.
CrossRef
J. Castro and J.L. Balcázar, Simple PAC learning of simple decision lists, in ALT 95, 6th International Workshop on Algorithmic Learning Theory. Springer, Lecture Notes in Comput. Sci. 997
(1995) 239-250.
Castro, J. and Guijarro, D., PACS, simple-PAC and query learning.
Inform. Process. Lett.
73 (2000) 11-16.
CrossRef
F. Denis, Learning regular languages from simple positive examples, Machine Learning. Technical Report LIFL 321 - 1998; http://www.lifl.fr/denis (to appear).
F. Denis, C. D'Halluin and R. Gilleron, PAC Learning with Simple Examples, in 13th Annual Symposium on Theoretical Aspects of Computer Science. Springer-Verlag, Lecture Notes in Comput. Sci. 1046
(1996) 231-242.
F. Denis and R. Gilleron, PAC learning under helpful distributions, in Proc. of the 8th International Workshop on Algorithmic Learning Theory (ALT-97), edited by M. Li and A. Maruoka. Springer-Verlag, Berlin, Lecture Notes in Comput. Sci. 1316
(1997) 132-145.
Gold, E.M., Complexity of Automaton Identification from Given Data.
Inform. and Control
37 (1978) 302-320.
CrossRef
Goldman, S.A. and Kearns, M.J., On the Complexity of Teaching.
J. Comput. System Sci.
50 (1995) 20-31.
CrossRef
Goldman, S.A. and Mathias, H.D., Teaching a Smarter Learner.
J. Comput. System Sci.
52 (1996) 255-267.
CrossRef
Hancock, T., Jiang, T., Li, M. and Tromp, J., Lower Bounds on Learning Decision Lists and Trees.
Inform. and Comput.
126 (1996) 114-122.
Haussler, D., Kearns, M., Littlestone, N. and Warmuth, M.K., Equivalence of Models for Polynomial Learnability.
Inform. and Comput.
95 (1991) 129-161.
CrossRef
Higuera, C.D.L., Characteristic Sets for Polynomial Grammatical Inference.
Machine Learning
27 (1997) 125-137.
CrossRef
M. Kearns, M. Li, L. Pitt and L.G. Valiant, Recent Results on Boolean Concept Learning, in Proc. of the Fourth International Workshop on Machine Learning (1987) 337-352.
M.J. Kearns and U.V. Vazirani, An Introduction to Computational Learning Theory. MIT Press (1994).
Li, M. and Vitányi, P.M.B., Learning simple concepts under simple distributions.
SIAM J. Comput.
20 (1991) 911-935.
CrossRef
M. Li and P. Vitányi, An introduction to Kolmogorov complexity and its applications, 2nd Edition. Springer-Verlag (1997).
D.H. Mathias, DNF: If You Can't Learn 'em, Teach 'em: An Interactive Model of Teaching, in Proc. of the 8th Annual Conference on Computational Learning Theory (COLT'95). ACM Press, New York (1995) 222-229.
B.K. Natarajan, Machine Learning: A Theoretical Approach. Morgan Kaufmann, San Mateo, CA (1991).
B.K. Natarajan, On Learning Boolean Functions, in Proc. of the 19th Annual ACM Symposium on Theory of Computing. ACM Press (1987) 296-304.
J. Oncina and P. Garcia, Inferring regular languages in polynomial update time, in Pattern Recognition and Image Analysis (1992) 49-61.
R. Parekh and V. Honavar, On the Relationships between Models of Learning in Helpful Environments, in Proc. Fifth International Conference on Grammatical Inference (2000).
R. Parekh and V. Honavar, Learning DFA from simple examples, in Proc. of the 8th International Workshop on Algorithmic Learning Theory (ALT-97), edited by M. Li and A. Maruoka. Springer, Berlin, Lecture Notes in Artificial Intelligence 1316
(1997) 116-131.
R. Parekh and V. Honavar, Simple DFA are polynomially probably exactly learnable from simple examples, in Proc. 16th International Conf. on Machine Learning (1999) 298-306.
Rivest, R.L., Learning Decision Lists.
Machine Learning
2 (1987) 229-246.
K. Romanik, Approximate Testing and Learnability, in Proc. of the 5th Annual ACM Workshop on Computational Learning Theory, edited by D. Haussler. ACM Press, Pittsburgh, PA (1992) 327-332.
S. Salzberg, A. Delcher, D. Heath and S. Kasif, Learning with a Helpful Teacher, in Proc. of the 12th International Joint Conference on Artificial Intelligence, edited by R. Myopoulos and J. Reiter. Morgan Kaufmann, Sydney, Australia (1991) 705-711.
Schapire, R.E., The Strength of Weak Learnability.
Machine Learning
5 (1990) 197-227.
A. Shinohara and S. Miyano, Teachability in Computational Learning. NEWGEN: New Generation Computing 8
(1991).