On the proper learning of axis-parallel concepts

Journal of Machine Learning Research

Volumn 4, Issue 2, 2004, Pages 157-176

  Bshouty, Nader H ^a   Burroughs, Lynn ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Axis parallel objects; Boolean formulas; Exact learning; Minimizing formula size; PAC learning

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DECISION THEORY; MATHEMATICAL MODELS; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING; TREES (MATHEMATICS);

AXIS-PARALLEL OBJECTS; BOOLEAN FORMULAS; DECISION TREE PARTITION; EXACT LEARNING;

LEARNING SYSTEMS;

EID: 2342592656     PISSN: 15324435     EISSN: None     Source Type: Journal    
DOI: 10.1162/153244304322972676     Document Type: Article

References (25)

1. D. Angluin. Queries and concept learning. Machine Learning, 2(4):319-342, 1987.
2. A. Beimel, F. Bergadano, N.H. Bshouty, E. Kushilevitz, and S. Varricchio. Learning functions represented as multiplicity automata. Journal of the ACM, 47(3):506-530, 2000.
3. A. Beimel and E. Kushilevitz. Learning boxes in high dimension. Algorithmica, 22(1/2):76-90, 1998.
4. S. Ben-David, N.H. Bshouty, and E. Kushilevitz. A composition theorem for learning algorithms with applications to geometric concept classes. In Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC), pages 324-333, 1997.
5. F. Bergadano, D. Catalano, and S. Varricchio. Learning sat-k-DNF formulas from membership queries. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC), pages 126-130, 1996.
6. P. Berman and B. DasGupta. On approximating the rectilinear polygon cover problems. In Proceedings of the 4th Canadian Conference on Computational Geometry, pages 229-235, 1992.
7. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Occam's razor. Information Processing Letters, 24(6):377-380, 1987.
8. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. Journal of the ACM, 36(4):929-965, 1989.
9. N. Bshouty. A new composition theorem for learning algorithms. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC), pages 583-589, 1998.
10. N.H. Bshouty. Exact learning Boolean functions via the monotone theory. Information and Computation, 123(1):146-153, 1995.
11. N.H. Bshouty, R. Cleve, R. Gavaldà, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences, 52(3):421-433, 1996.
12. N.H. Bshouty, P.W. Goldberg, S.A. Goldman, and D.H. Mathias. Exact learning of discretized geometric concepts. SIAM Journal of Computing, 28(2):674-699, 1998.
13. Z. Chen and S. Homer. The bounded injury priority method and the learnability of unions of rectangles. Annals of Pure and Applied Logic, 77(2): 143-168, 1996.
14. Z. Chen and W. Maass. On-line learning of rectangles and unions of rectangles. Machine Learning, 17(2 and 3):201-223, 1994.
15. V. Dielissen and A. Kaldewaij. Rectangular partition is polynomial in two dimensions but NP-complete in three. Information Processing Letters, 38(1): 1-6, 1991.
16. D. Haussler, M. Kearns, N. Littlestone, and M. Warmuth. Equivalence of models for polynomial learnability. Information and Computation, 95(2):129-161, 1991.
17. L. Hellerstein, K. Pillaipakkamnatt, V. Raghavan, and D. Wilkins. How many queries are needed to learn? Journal of the ACM, 43(5):840-862, 1996.
18. L. Hellerstein and V. Raghavan. Exact learning of DNF formulas using DNF hypotheses. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC), 2002.
19. õ(n1/3) In Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC), pages 258-265, 2001.
20. W. Lipski Jr., E. Lodi, F. Luccio, C. Mugnai, and L. Pagli. On two-dimensional data organization II. Fundamenta Informaticae, 2:245-260, 1979.
21. W. Maass and M.K. Warmuth. Efficient learning with virtual threshold gates. Information and Computation, 141(1):66-83, 1998.
22. K. Pillaipakkamnatt and V. Raghavan. On the limits of proper learnability of subclasses of DNF formulas. Machine Learning, 25(2 and 3):237-263, 1996.
23. R.E. Schapire and L.M. Sellie. Learning sparse multivariate polynomials over a field with queries and counterexamples. In Proceedings of the Sixth Annual ACM Conference on Computational Learning Theory (COLT), pages 17-26, 1993.
24. p minimization problems. In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 465-474, 1999.
25. H. Zantema and H. Bodlaender. Finding small equivalent decision trees is hard. International Journal of Foundations of Computer Science, 11(2):343-354, 2000.