Abstract
Valiant argued that biology imposes various constraints on learnability, and, motivated by these constraints, introduced his model of projection learning [14]. Projection learning aims to learn a target concept over some large domain, in this paper {0,1}n, by learning some of its projections to a class of smaller domains, and combining these projections. Valiant proved a general mistake bound for the resulting algorithm under certain conditions. The basic assumption underlying projection learning is that there is a family of simple projections that cover all positive instances of the target, where simple means belonging to some efficiently learnable class. The projections describing the target in this way can also be thought of as a set of experts, each specialized to classify a subset of the instances, such that whenever two experts overlap they always agree in their classification.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angluin, D.: Queries revisited. In: Abe, N., Khardon, R., Zeugmann, T. (eds.) ALT 2001. LNCS (LNAI), vol. 2225, pp. 12–31. Springer, Heidelberg (2001)
Auer, P., Warmuth, M.K.: Tracking the best disjunction. Machine Learning 32(2), 127–150 (1998); Earlier version in 36th FOCS (1995)
Blum, A.: On-line algorithms in machine learning (1996), Available from http://www-2.cs.cmu.edu/~avrim/Papers/pubs.html
Goldsmith, J., Sloan, R.H., Szörényi, B., Turán, G.: Theory revision with queries: Horn, read-once, and parity formulas. Technical Report TR03-039, Electronic Colloquium on Computational Complexity (ECCC) (2003) (Also submitted for journal publication), Available at http://www.eccc.uni-trier.de/eccc/
Goldsmith, J., Sloan, R.H., Turán, G.: Theory revision with queries: DNF formulas. Machine Learning 47(2/3), 257–295 (2002)
Hegedüs, T.: Generalized teaching dimensions and the query complexity of learning. In: Proc. 8th Annu. Conf. on Comput. Learning Theory, pp. 108–117. ACM Press, New York (1995)
Hellerstein, L., Pillaipakkamnatt, K., Raghavan, V., Wilkins, D.: How many queries are needed to learn? J. ACM 43(5), 840–862 (1996)
Helmbold, D., Sloan, R., Warmuth, M.K.: Learning nested differences of intersection closed concept classes. Machine Learning 5(2), 165–196 (1990); Special Issue on Computational Learning Theory, first appeared in 2nd COLT conference (1989)
Kivinen, J., Warmuth, M.K.: Additive versus exponentiated gradient updates for linear prediction. In: Proc. 27th Annual ACM Symposium on Theory of Computing, pp. 209–218. ACM Press, New York (1995)
Littlestone, N.: Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm. Machine Learning 2(4), 285–318 (1988)
Littlestone, N.: A mistake-bound version of Rivest’s decision-list algorithm. Personal communication to Avrim Blum (1989)
Mesterharm, C.: Tracking linear-threshold concepts with Winnow. In: Kivinen, J., Sloan, R.H. (eds.) COLT 2002. LNCS (LNAI), vol. 2375, pp. 138–152. Springer, Heidelberg (2002)
Rivest, R.L.: Learning decision lists. Machine Learning 2, 229–246 (1987)
Valiant, L.G.: Projection learning. Machine Learning 37(2), 115–130 (1999)
Valiant, L.G.: A neuroidal architecture for cognitive computation. Journal of the ACM 47(5), 854–882 (2000)
Wrobel, S.: Concept Formation and Knowledge Revision. Kluwer, Dordrecht (1994)
Wrobel, S.: First order theory refinement. In: De Raedt, L. (ed.) Advances in ILP, pp. 14–33. IOS Press, Amsterdam (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sloan, R.H., Szörényi, B., Turán, G. (2003). Projective DNF Formulae and Their Revision. In: Schölkopf, B., Warmuth, M.K. (eds) Learning Theory and Kernel Machines. Lecture Notes in Computer Science(), vol 2777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45167-9_45
Download citation
DOI: https://doi.org/10.1007/978-3-540-45167-9_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40720-1
Online ISBN: 978-3-540-45167-9
eBook Packages: Springer Book Archive