Efficient Learning with Virtual Threshold Gates

Information and Computation

Volumn 141, Issue 1, 1998, Pages 66-83

  Maass, Wolfgang ^a   Warmuth, Manfred K ^b  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001784922     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.1997.2686     Document Type: Article

References (36)

1. Aho, Alfred V., Hopcroft, John E., and Ullman, Jeffrey D. (1974), "The Design and Analysis of Computer Algorithms," Addison-Wesley, Reading, MA.
2. Angluin, Dana (1988), Queries and concept learning, J. Mach. Learning 2(4), 319-342.
3. Auer, P., Kwek, S., Maass, W., and Warmuth, M. K. (1996), Learning of depth two neural networks with constant fan-in at the hidden nodes, in "Proc. 9th Annu. Conf. on Comput. Learning Theory," pp. 333-343, Assoc. Comput. Mach. Press, New York.
4. Auer, P., and Long, P. M. (1994), Simulating access to hidden information while learning, in "Proceedings of the 26th ACM Symposium on the Theory of Computation," pp. 263-272, Assoc. Comput. Mach. Press.
5. Auer, P., and Warmuth, M. K. (1995), Tracking shifting disjunctions, in "Proc. 36th Annual Symposium on Foundations of Computer Science," pp. 312-321, IEEE Computer Society Press, Los Alamitos, CA.
6. Auer, P. (1993), Online learning of rectangles in noisy environments, in "Proceedings of the Sixth Annual ACM Conference on Computational Learning Theory," pp. 253-261.
7. Blumer, Anselm, Ehrenfeucht, Andrzej, Haussler, David, and Warmuth, Manfred K. (1989), Learnability and the Vapnik-Chervonenkis dimension, J. Assoc. Comput. Mach. 36(4), 929-965.
8. Bshouty, Nader, H., Goldberg, Paul W., Goldman, Sally A., and Mathias, H. David (1994), "Exact Learning of Discretized Concepts," Technical Report WUCS-94-19, Washington University.
9. Bshouty, Nader H., Chen, Zhixiang, and Homer, Steve (1994), On learning discretized geometric concepts, in "Proc. 35th Annual Symposium on Foundations of Computer Science," pp. 54-63, IEEE Computer Society Press, Los Alamitos, CA.
10. Chen, Zhixiang, and Homer, Steven (1996), The bounded injury priority method and the learnability of unions of rectangles, Ann. Pure Appl. Logic 77, 143-168.
11. Chen, Zhixiang, and Maass, Wolfgang (July 1992), Online learning of rectangles, in "Proceedings of the Fifth Annual Workshop on Computational Learning Theory," pp. 16-27, Assoc. Comput. Mach. Press. [Also in (1994), Machine Learning 17, 201-223.]
12. Chen, Zhixiang, and Maass, Wolfgang (July 1992), Online learning of rectangles, in "Proceedings of the Fifth Annual Workshop on Computational Learning Theory," pp. 16-27, Assoc. Comput. Mach. Press. [Also in (1994), Machine Learning 17, 201-223.]
13. Cover, T. (1991), Universal portfolios, Math. Finance 1(1), 1-29.
14. Dichterman, E., and Khardon, R., A tight bound for the VC dimension of k-term DNF, private communication.
15. Frazier, Mike, Goldman, Sally, Mishra, Nina, and Pitt, Leonard (1996), Learning from a consistently ignorant teacher, J. Comput. System Sci. 52(3), 472-492.
16. Haussler, David (1989), Learning conjunctive concepts in structural domains, Mach. Learning 4(1), 7-40.
17. Haussler, D., Kivinen, J., and Warmuth, M. K., Tight worst-case loss bounds for predicting with expert advice, IEEE Trans. Inform. Theory, to appear.
18. Helmbold, D. P., and Schapire, R. E. (1997), Predicting nearly as well as the best pruning of a decision tree, Mach. Learning 27, 51-68.
19. Helmbold, D. P., Sloan, R., and Warmuth, Manfred K. (1990), Learning nested differences of intersection-closed concept classes, Mach. Learning 5, 165-196.
20. Herbster, M., and Warmuth, M. K. (1995), Tracking the best expert, in "Proc. of the Twelfth International Conference on Machine Learning," pp. 286-294, Morgan Kaufmann, San Francisco.
21. Kearns, M. J., and Vazirani, U. V. (1994), "An Introduction to Computational Learning Theory," MIT Press, Cambridge, MA.
22. Kivinen, J., and Warmuth, M. K. (1997), Exponentiated gradient versus gradient descent for linear predictors, Inform. and Comput. 132, 1-64.
23. Kivinen, J., Warmuth, M. K., and Auer, P., The Perceptron algorithm vs. Winnow: linear vs. logarithmic mistake bounds when few input variables are relevant, Artificial Intelligence, to appear in the special issue on Relevance.
24. Littlestone, N. (1988), Learning when irrelevant attributes abound: A new linear-threshold algorithm, Mach. Learning 2, 285-318.
25. Littlestone, N. (1989), "Mistake Bounds and Logarithmic Linear-threshold Learning Algorithms," Ph.D. thesis, University of California Santa Cruz. [Technical Report UCSC-CRL-89-11]
26. Littlestone, N. (1989), From online to batch learning, in "Proceedings of the Second Annual Workshop on Computational Learning Theory," pp. 269-284, Morgan Kaufmann, San Mateo, CA.
27. Littlestone, N. (1991), Redundant noisy attributes, attribute errors, and linear threshold learning using Winnow, in "Proc. 4th Annu. Workshop on Comput. Learning Theory," pp. 147-156, Morgan Kaufmann, San Mateo, CA.
28. Littlestone, N., private communication.
29. Littlestone, N., and Warmuth, M. K. (1994), The weighted majority algorithm, Inform. and Comput. 108, 212-261.
30. Maass, Wolfgang, and Turán, György (1994), Algorithms and lower bounds for online learning of geometrical concepts, Mach. Learning 14, 251-269.
31. Maass, Wolfgang, and Turán, Györgi (1992), Lower bound methods and separation results for online learning models, Mach. Learning 9, 107-145.
32. Rosenblatt, F. (1958), The perceptron: A probabilistic model for information storage and organization in the brain, Psych. Rev. 65, 386-407. [Reprinted in "Neurocomputing", MIT Press, 1988]
33. Rosenblatt, F. (1958), The perceptron: A probabilistic model for information storage and organization in the brain, Psych. Rev. 65, 386-407. [Reprinted in "Neurocomputing", MIT Press, 1988]
34. Valiant, L. G. (1984), A theory of the learnable, Commun. Assoc. Comput. Mach. 27(11), 1134-1142.
35. Vapnik, V. N., and Chervonenkis, A. Y. (1971), On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Appl. 16(2), 264-280.
36. Vovk, V. (1990), Aggregating strategies, in "Proc. 3rd Workshop on Computational Learning Theory," pp. 371-383, Morgan Kaufmann, San Mateo, CA.