Abstract
We study functions with multiple output values, and use active sampling to identify an example for each of the possible output values. Our results for this setting include: (1) Efficient active sampling algorithms for simple geometric concepts, such as intervals on a line and axis parallel boxes. (2) A characterization for the case of binary output value in a transductive setting. (3) An analysis of active sampling with uniform distribution in the plane. (4) An efficient algorithm for the Boolean hypercube when each output value is a monomial.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dasgupta, S.: Analysis of a greedy active learning strategy. In: Advances in Neural Information Processing Systems (NIPS) (2004)
Dasgupta, S.: Coarse sample complexity bounds for active learning. In: Advances in Neural Information Processing Systems (NIPS) (2005)
Dasgupta, S., Kalai, A.T., Monteleoni, C.: Analysis of perceptron-based active learning. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS, vol. 3559, pp. 249–263. Springer, Heidelberg (2005)
Edelstein, O., Farchi, E., Nir, Y., Ratzaby, G., Ur, S.: Multithreaded java program test generation. IBM Systems Journal 41(3), 111–125 (2002)
Efron, B.: The convex hull of a rndom set of points. Biometrika 52, 331–343 (1965)
Fine, S., Gilad-Bachrach, R., Shamir, E.: Query by committee, linear separation and random walks. Theoretical Computer Science 284(1) (2002), (A preliminary version appeared in EuroColt 1999)
Fine, S., Ziv, A.: Coverage directed test generation for functional verification using Bayesian networks. In: Proceedings of the 40th Design Automation Conference, pp. 286–291 (June 2003)
Freund, Y., Seung, H., Shamir, E., Tishby, N.: Selective sampling using the query by committee algorithm. Machine Learning 28(2/3), 133–168 (1997)
Kulkarni, S.R., Mitter, S.K., Tsitsiklis, J.N.: Active learning using arbitrary binary valued queries. Machine Learning 11, 23–35 (1993)
Liere, R., Tadepalli, P.: Active learning with committees for text categorization. In: AAAI 1997 (1997)
Linial, N., Luby, M., Saks, M., Zuckerman, D.: Efficient construction of a small hitting set for combinatorial rectangles in high dimension. Combinatorica 17(2), 215–234 (1997), (A preliminary version appeard in STOC 1993)
Piziali, A.: Functional Verification Coverage Measurement and Analysis. Springer, Heidelberg (2004)
Preparata, F.P., Shamos, M.I.: Computational Geometry: An introduction. Springer, Heidelberg (1985)
Rényi, A., Sulamke, R.: Uber die konvexe hulle von n zufallig gewahlten punkten. Z. Wahrschein 2, 75–84 (1963)
Sauer, N.: On the density of family of sets. J. of Combinatorial Theory, Ser. A 13, 145–147 (1972)
Seung, H.S., Opper, M., Sompolinsky, H.: Query by committe. In: Proceedings of the Fith Workshop on Computational Learning Theory, pp. 287–294. Morgan Kaufman, San Mateo (1992)
Ur, S., Yadin, Y.: Micro-architecture coverage directed generation of test programs. In: Proceedings of the 36th Design Automation Conference, June 1999, pp. 175–180 (1999)
Vapnik, V.N., Ya, A.: Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its applications XVI(2), 264–280 (1971)
Wile, B., Goss, J.C., Roesner, W.: Comprehensive Functional Verification – The Complete Industry Cycle. Elsevier, Amsterdam (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fine, S., Mansour, Y. (2006). Active Sampling for Multiple Output Identification. In: Lugosi, G., Simon, H.U. (eds) Learning Theory. COLT 2006. Lecture Notes in Computer Science(), vol 4005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11776420_45
Download citation
DOI: https://doi.org/10.1007/11776420_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35294-5
Online ISBN: 978-3-540-35296-9
eBook Packages: Computer ScienceComputer Science (R0)