Every linear threshold function has a low-weight approximator

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn 2006, Issue , 2006, Pages 18-30

  Servedio, Rocco A ^a  

^a Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGER WEIGHTS; INVERSE POLYNOMIALS; LINEAR THRESHOLD FUNCTION; POLYNOMIAL BOUNDS;

APPROXIMATION ALGORITHMS; INTEGER PROGRAMMING; INVERSE PROBLEMS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING;

BOOLEAN FUNCTIONS;

EID: 34247484531     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2006.18     Document Type: Conference Paper

References (42)

1. S. Ben-David and E. Dichterman. Learnability with restricted focus of attention guarantees noise-tolerance. In Proceedings of the 5th International Workshop on Algorithmic Learning Theory, pages 248-259, 1994.
2. S. Ben-David and E. Dichterman. Learning with restricted focus of attention. Journal of Computer and System Sciences, 56(3):277-298, 1998.
3. A. Birkendorf, E. Dichterman, J. Jackson, N. Klasner, and H. Simon. On restricted-focus-of-attention learnability of boolean functions. Machine Learning, 30:89-123, 1998.
4. H. Block. The Perceptron: a model for brain functioning. Reviews of Modern Physics, 34:123-135, 1962.
5. J. Brack. Harmonic analysis of polynomial threshold functions. SIAM Journal on Discrete Mathematics, 3(2): 168-177, 1990.
6. C. Chow. On the characterization of threshold functions. In Proceedings of the Symposium on Switching Circuit Theory and Logical Design, pages 34-38, 1961.
7. M. Dertouzos. Threshold logic: a synthesis approach. MIT Press, Cambridge, MA, 1965.
8. M. Dyer. Approximate counting by dynamic programming. In Proceedings of the 35th Annual Symposium on Theory of Computing (STOC), pages 693-699, 2003.
9. M. Dyer, A. Frieze, K. Rannan, A. Kapoor, L. Perkovic, and U. Vazirani. A mildly exponential time algorithm for approximating the number of solutions to a multidimensional knapsack problem. Combinatorics, Probability and Computing, 2:271-284, 1993.
10. Y. Freund. Boosting a weak learning algorithm by majority. Information and Computation, 121(2):256-285, 1995.
11. Y. Freund and R. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 55(1): 119-139, 1997.
12. P. Goldberg. Estimating a boolean perceptron from its average satisfying assignment: A bound on the precision required. In Proceedings of the Fourteenth Annual Conference on Computational Learning Theory, pages 116-127, 2001.
13. M. Goldmann, J. Håstad, and A. Razborov. Majority gates vs. general weighted threshold gates. Computational Complexity, 2:277-300, 1992.
14. M. Goldmann and M. Karpinski. Simulating threshold circuits by majority circuits. SIAM Journal on Computing, 27(1):230-246, 1998.
15. A. Hajnal, W. Maass, P. Pudlak, M. Szegedy, and G. Turan. Threshold circuits of bounded depth. Journal of Computer and System Sciences, 46:129-154, 1993.
16. J. Håstad. On the size of weights for threshold gates. SIAM Journal on Discrete Mathematics, 7(3):484-492, 1994.
17. J. Håstad. Personal communication, 2005.
18. T. Hofmeister. A note on the simulation of exponential threshold weights. In Computing and Combinatorics, Second Annual International Conference (COCOON), pages 136-141, 1996.
19. J. Hong. On connectionist models. Technical Report Technical Report 87-012, Dept. of Computer Science, University of Chicago, 1987.
20. S. Hu. Threshold Logic. University of California Press, 1965.
21. M. Jerrum and A. Sinclair. The Markov Chain Monte Carlo method: an approach to approximate counting and integration, pages 482-520. PWS Publishing, 1997.
22. R. Kannan. Markov chains and polynomial time algorithms. In Proceedings of the 35th Symposium on Foundations of Computer Science, pages 656-671, 1994.
23. P. Kaszerman. A gemoetric test-synthesis procedure for a threshold device. Information and Control, 6(4):381-398, 1963.
24. A. Klivans, R. O'Donnell, and R. Servedio. Learning intersections and thresholds of halfspaces. Journal of Computer & System Sciences, 68(4):808-840, 2004. Preliminary version in Proc. of FOCS'02.
25. Õ(n1/3). In Proceedings of the Thirty-Third Annual Symposium on Theory of Computing, pages 258-265, 2001.
26. S. Kulkarni, S. Mitter, and J. Tsitsiklis. Active learning using arbitrary binary valued queries. Machine Learning, 11:23-35, 1993.
27. N. Littlestone. Learning quickly when irrelevant attributes abound: a new linear-threshold algorithm. Machine Learning, 2:285-318, 1988.
28. N. Littlestone. Redundant noisy attributes, attribute errors, and linear-threshold learning using Winnow. In Proceedings of the Fourth Annual Workshop on Computational Learning Theory, pages 147-156, 1991.
29. W. Maass and G. Turan. How fast can a threshold gate learn?, pages 381-414. MIT Press, 1994.
30. B. Morris and A. Sinclair. Random walks on truncated cubes and sampling 0-1 knapsack solutions (preliminary version). In Proceedings of the 40th Annual Symposium on Foundations of Computer Science (FOCS), pages 230-240, 1999.
31. S. Muroga. Threshold logic and its applications. Wiley-Interscience, New York, 1971.
32. S. Muroga, I. Toda, and S. Takasu. Theory of majority switching elements. J. Franklin Institute, 271:376-418, 1961.
33. A. Novikoff. On convergence proofs on perceptrons. In Proceedings of the Symposium on Mathematical Theory of Automata, volume XII, pages 615-622, 1962.
34. P. Orponen. Neural networks and complexity theory. In Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science, pages 50-61, 1992.
35. V. V. Petrov. Limit theorems of probability theory. Oxford Science Publications, Oxford, England, 1995.
36. P. Raghavan. Learning in threshold networks. In First Workshop on Computational Learning Theory, pages 19-27, 1988.
37. A. Razborov. On small depth threshold circuits. In Proceedings of the Third Scandinavian Workshop on Algorithm Theory (SWAT), pages 42-52, 1992.
38. R. Servedio. Monotone Boolean Formulas can Approximate Monotone Linear Threshold Functions. Discrete Applied Mathematics, 142(1-3):181-187, 2004.
39. J. Shawe-Taylor and N. Cristianini. An introduction to support vector machines. Cambridge University Press, 2000.
40. L. Trevisan. A note on approximate counting for k-dnf. In Proceedings of the Eighth International Workshop on Randomization and Computation, pages 417-426, 2004.
41. L. Valiant. Short monotone formulae for the majority function. Journal of Algorithms, 5:363-366, 1984.
42. R. Winder. Chow parameters in threshold logic. Journal of the ACM, 18(2):265-289, 1971.