The capacity of majority rule

Random Structures and Algorithms

Volumn 12, Issue 1, 1998, Pages 83-109

  Fang, Shao C ^a   Venkatesh, Santosh S ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Binary integer programming; Capacity; Majority rule; Neuron; Perceptron; Random polytopes; Threshold function

Indexed keywords

EID: 0032327797     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199801)12:1<83::AID-RSA5>3.0.CO;2-P     Document Type: Article

References (12)

1. S. C. Fang and S. S. Venkatesh, On the average tractability of binary integer programming and the curious transition to perfect generalizaton in learning majority functions, Proceedings of the Sixth ACM Conference on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, 1993, pp. 310-316.
2. S. C. Fang and S. S. Venkatesh, Learning binary perceptrons perfectly efficiently, J. Comput. System Sci., 52, 374-389 (1996).
3. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, 3rd ed., Wiley, New York, 1968.
4. Z. Füredi, Random polytopes in the d-dimensional cube, Discrete Comput. Geom., 1, 315-319 (1986).
5. M. Garey and D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
6. N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, 4, 373-395 (1984).
7. L. Pitt and L. G. Valiant, Computational limitations on learning from examples, J. Assoc. Comput. Mach., 35, 965-984 (1988).
8. W. Richter, Multidimensional local limit theorems for large deviations, Theory Probab. Appl., 3, 100-106 (1958).
9. H. Ruben, An asymptotic expansion for a class of multivariate normal integrals, J. Austral. Math. Soc., 2, 253-264 (1962).
10. S. S. Venkatesh, On learning binary weights for majority functions, Proceedings of the Fourth Annual Workshop on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, 1991.
11. S. S. Venkatesh, Computation and learning in the context of neural network capacity, in Neural Networks for Perception, H. Wechsler, Ed., Academic Press, New York, 1991.
12. S. S. Venkatesh, Directed drift: a new linear threshold algorithm for learning binary weights on-line, J. Comput. System Sci., 46, 198-217 (1993).