Geometric & topological representations of maximum classes with applications to sample compression

21st Annual Conference on Learning Theory, COLT 2008

Volumn , Issue , 2008, Pages 299-310

  Rubinstein, Benjamin I P ^a   Rubinstein, J Hyam ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CUBICAL COMPLEX; EUCLIDEAN SPACES; HYPERBOLIC SPACES; HYPERPLANE ARRANGEMENTS; PIECEWISE-LINEAR; SAMPLE COMPRESSION; TOPOLOGICAL REPRESENTATION; UNLABELED COMPRESSION;

PIECEWISE LINEAR TECHNIQUES;

GEOMETRY;

EID: 77952428272     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. N. Alon. On the density of sets of vectors. Discrete Math., 46(2): 199-202, 1983.
2. S. Ben-David and A. Litman. Combinatorial variability of Vapnik-Chervonenkis classes with applications to sample compression schemes. Discrete Applied Math., 86(1): 3-25, 1998.
3. A. Blumer, A. Ehrenfeucht, D. Haussler, and M.K. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. Journal of the ACM, 36(4): 929-965, 1989.
4. R.M. Dudley. The structure of some Vapnik-Chervonenkis classes. In L.M. Le Cam and R.A. Olshen, editors, Proceedings of the Berkeley Conference in Honor of Jerzy Neyman, volume II, pages 495-507. Wadsworth, 1985.
5. H. Edelsbrunner. Algorithms in Combinatorial Geometry, volume 10 of EATCS Monographs on Theoretical Computer Science. SpringerVerlag, 1987.
6. S. Floyd. Space-bounded learning and the Vapnik-Chervonenkis dimension. Technical Report TR-89-061, ICSI, UC Berkeley, 1989.
7. P. Frankl. On the trace of finite sets. Journal of Comb. Theory (A), 34(1): 41-45, 1983.
8. B. Gärtner and E. Welzl. Vapnik-Chervonenkis dimension and (pseudo-) hyperplane arrangements. Discrete and Comp. Geometry, 12: 399-432, 1994.
9. D. Haussler. Sphere packing numbers for subsets of the boolean n-cube with bounded Vapnik-Chervonenkis dimension. Journal of Comb. Theory (A), 69: 217-232, 1995.
10. D. Haussler, N. Littlestone, and M.K. Warmuth. Predicting {0, 1} functions on randomly drawn points. Information and Computation, 115(2): 284-293, 1994.
11. D. Kuzmin and M.K. Warmuth. Unla-beled compression schemes for maximum classes. Journal of Machine Learning Research, 8(Sep): 2047-2081, 2007.
12. N. Littlestone and M.K. Warmuth. Relating data compression and learnability. Unpublished manuscript, 1986.
13. B. Mazur. A note on some contractible 4-manifolds. Annals of Math., 73: 221-228, 1961.
14. T. Neylon. Sparse Solutions for Linear Prediction Problems. PhD thesis, NYU, 2006.
15. J. G. Ratcliffe. Foundations of Hyperbolic Manifolds. Springer-Verlag, 1994.
16. B. I. P. Rubinstein, P. L. Bartlett, and J. H. Rubinstein. Shifting: one-inclusion mistake bounds and sample compression. Journal of Computer and System Sciences: Special Issue on Learning Theory 2006, 2008. in press.
17. C. Rourke and B. Sanderson. Introduction to Piecewise-Linear Topology. Springer-Verlag, 1982.
18. N. Sauer. On the density of families of sets. Journal of Comb. Th. (A), 13: 145-147, 1972.
19. S. Shelah. A combinatorial problem; stability and order for models and theories in infinitary languages. Pacific Journal of Math., 41(1): 247-261, 1972.
20. S. Smale. Generalized Poincaré conjecture in dimensions greater than four. Annals of Math., 74: 391-406, 1961.
21. V. N. Vapnik and A. Y. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory of Prob. and its Applic., 16(2): 264-280, 1971.
22. M.K. Warmuth. Compressing to VC dimension many points. In Proceedings of the 16th Annual Conference on Learning Theory, 2003.
23. E. Welzl. Complete range spaces. Unpublished notes, 1987.