On hardness of learning intersection of two halfspaces

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2008, Pages 345-353

  Khot, Subhash ^a   Saket, Rishi ^a  

^a Georgia Tech

Author keywords

Approximation; Halfspaces; Hardness; Learning

Indexed keywords

GEOMETRY; HARDNESS; POLYNOMIAL APPROXIMATION;

APPROXIMATION; HALF SPACES; HARDNESS OF LEARNING; LEARNING; LINEAR THRESHOLD FUNCTIONS; POLYNOMIAL-TIME ALGORITHMS;

COMPUTATION THEORY;

EID: 57049098727     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1374376.1374426     Document Type: Conference Paper

References (26)

1. th IEEE FOGS, pages 621-630, 2004.
2. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. J. ACM, 45(3):501-555, 1998.
3. S. Arora and S. Safra. Probabilistic checking of proofs: A new characterization of NP. J. ACM, 45(1):70-122, 1998.
4. th IEEE FOCS, pages 616-623, 1999.
5. I. Benjamin, G. Kalai, and O. Schramm. Noise sensitivity of boolean functions and applications to percolation. Inst. Hautes Études Sci. Publ. Math., (90):5-43, 1999.
6. th IEEE FOCS, pages 330-338, 1996.
7. A. Blum and R. Kannan. Learning an intersection of a constant number of halfspaces over a uniform distribution. J. Comput. Syst. Sci., 54(2):371-380, 1997.
8. A. Blum and R. Rivest. Training a 3-node neural network is NP-complete. In Proc. Machine Learning: From Theory to Applications, pages 9-28, 1993.
9. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Learnability and the Vapnik Chervonenkis dimension. J. ACM, 36(4):929-965, 1989.
10. th IEEE FOCS, pages 563-574, 2006.
11. th IEEE FOCS, pages 349-359, 2007.
12. th IEEE FOCS, pages 543-552, 2006.
13. th ACM STOC, pages 11-20, 2004.
14. th IEEE FOCS, pages 11-20, 2005.
15. rd IEEE FOCS, pages 23-32, 2002.
16. S. Khot and R. Saket. A 3-query non-adaptive PGP with perfect completeness. In Proc. IEEE CCC, pages 159-169, 2006.
17. rd IEEE FOCS, pages 177-186, 2002.
18. A. Klivans and R. Servedio. Learning intersections of halfspaces with a margin. In Proc. COLT, pages 348-362, 2004.
19. th IEEE FOCS, pages 553-562, 2006.
20. A. Levin and A. Shashua. Principal component analysis over continuous subspaces and intersection of half-spaces. In Proc. ECCCV(S), pages 635-650, 2002.
21. D. Murphy. Nearest neighbor pattern classification perceptrons. Proceedings of the IEEE, 78(10):1595-1598, 1990.
22. R. Raz. A parallel repetition theorem. SIAM J. Comput., 27(3):763-803, 1998.
23. U. Rückert, L. Richter, and S. Kramer. Quantitative association rules based on half-spaces: An optimization approach. In Proc. ICDM, pages 507-510, 2004.
24. R. Schapire. The strength of weak learnability. Machine Learning, 5:197-227, 1990.
25. V. Vapnik and A. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications, 16(2):264-280, 1971.
26. th IEEE FOCS, pages 508-513, 1997.