Years and Authors of Summarized Original Work
1995; Hellerstein, Pilliapakkamnatt, Raghavan, Wilkins
Problem Definition
This problem concerns the query complexity of proper learning in a widely studied learning model: exact learning with membership and equivalence queries. Hellerstein et al. [10] showed that the number of (polynomially sized) queries required to learn a concept class in this model is closely related to the size of certain certificates associated with that class. This relationship gives a combinatorial characterization of the concept classes that can be learned with polynomial query complexity. Similar results were shown by Hegedüs based on the work of Moshkov [8, 13].
The Exact Learning Model
Concepts are functions f : X → { 0, 1} where X is an arbitrary domain. In exact learning, there is a hidden concept f from a known class of concepts C, and the problem is to exactly identify the concept f.
Algorithms in the exact learning model obtain information about f, the...
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Recommended Reading
Alekhnovich M, Braverman M, Feldman V, Klivans AR, Pitassi T (2004) Learnability and automatizability. In: Proceedings of the 45th annual IEEE symposium on foundations of computer science (FOCS ’04), Rome. IEEE Computer Society, Washington, DC, pp 621–630
Angluin D (1987) Queries and concept learning. Mach Learn 2(4):319–342
Angluin D (2004) Queries revisited. Theor Comput Sci 313(2):175–194
Balcan N, Hanneke S (2012) Robust interactive learning. In: Proceedings of the twenty fifth annual conference on learning theory (COLT ’12), Edinburgh, pp 20.1–20.34
Balcázar JL, Castro J, Guijarro D, Köbler J, Lindner W (2007) A general dimension for query learning. J Comput Syst Sci 73(6):924–940
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Feldman V (2006) Hardness of approximate two-level logic minimization and PAC learning with membership queries. In: Proceedings of the 38th annual ACM symposium on the theory of computing (STOC ’06), Seattle. ACM, New York, pp 363–372
Hegedüs T (1995) Generalized teaching dimensions and the query complexity of learning. In: Proceedings of the 8th annual conference on computational learning theory (COLT ’95), Santa Cruz, pp 108–117
Hellerstein L, Raghavan V (2005) Exact learning of DNF formulas using DNF hypotheses. J Comput Syst Sci 70(4):435–470
Hellerstein L, Pillaipakkamnatt K, Raghavan V, Wilkins D (1996) How many queries are needed to learn? J ACM 43(5):840–862
Hellerstein L, Kletenik D, Sellie L, Servedio R (2012) Tight bounds on proper equivalence query learning of DNF. In: Proceedings of the 25th annual conference on learning theory (COLT ’12), Edinburgh, pp 31.1—31.18
Köbler J, Lindner W (2000) Oracles in \(\Sigma ^{\text{p}}_{2}\) are sufficient for exact learning. Int J Found Comput Sci 11(4):615–632
Moshkov MY (1983) Conditional tests. Probl Kibern (in Russian) 40:131–170
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Hellerstein, L. (2016). Certificate Complexity and Exact Learning. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_66
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DOI: https://doi.org/10.1007/978-1-4939-2864-4_66
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