PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples

Machine Learning

Volumn 30, Issue 1, 1998, Pages 7-21

  Long, Philip M ^a   Tan, Lei ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b NONE   (United States)

Author keywords

Axis aligned hyperrectangles; Multiple instance examples; PAC learning

Indexed keywords

ALGORITHMS; DRAWING (GRAPHICS); MATHEMATICAL MODELS; POLYNOMIALS; PROBABILITY;

HYPERRECTANGLES; MULTIPLE INSTANCE EXAMPLES; PAC MODEL; PRODUCT DISTRIBUTIONS;

LEARNING SYSTEMS;

EID: 0031701616     PISSN: 08856125     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007450326753     Document Type: Article

References (13)

1. Auer, P., Long, P.M. & Srinivasan, A. (1997). Approximating hyper-rectangles: learning and pseudo-random sets. Proceedings of the 29th ACM Symposium on the Theory of Computing.
2. Blum, A. & Kalai, A. (this issue). A note on learning from multiple-instance examples. Machine Learning.
3. Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuthm M.K. (1989). Learnability and the Vapnik-Chervonenkis dimension. JACM, 36(4):929-965.
4. Dietterich, T.G., Lathrop, R.H. & Lozano-Perez, T. (1997). Solving the multiple-instance problem with axis-parallel rectangles. Artificial Intelligence, 89(1-2):31-71.
5. Ehrenfeucht, A., Haussler, D., Kearns, M. & Valiant, L.G. (1989). A general lower bound on the number of examples needed for learning. Information and Computation, 82(3):247-251.
6. Kearns, M.J. (1993). Efficient noise-tolerant learning from statistical queries. Proceedings of the 25th ACM Symposium on the Theory of Computing.
7. Kearns, M.J. & Schapire, R..E. (1994). Efficient distribution-free learning of probabilistic concepts. Journal of Computer and System Sciences, 48(3):464-497.
8. Long, P.M. & Tan, L. (1996). PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. The 1995 Conference on Computational Learning Theory, pages 228-234, 1996.
9. Long, P.M. & Warmuth, M.K. (1994). Composite geometric concepts and polynomial predictability. Information and Computation, 113(2):203-252.
10. Pitt, L. & Valiant, L.G. (1988). Computational limitations on learning from examples. Journal of the Association for Computing Machinery, 35(4):965-984.
11. Pollard, D. (1984). Convergence of Stochastic Processes. Springer Verlag.
12. Valiant, L.G. (1984). A theory of the learnable. Communications of the ACM, 27(11):1134-1142.
13. Yamanishi, K. (1992). A learning criterion for stochastic rules. Machine Learning. Special Issue on the Proceedings of the 3nd Workshop on Computational Learning Theory, to appear.