Communications of the ACM
How to construct random functions
Journal of the ACM (JACM)
Learning k-term DNF formulas with an incomplete membership oracle
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Exact identification of read-once formulas using fixed points of amplification functions
SIAM Journal on Computing
Learning decision trees using the Fourier spectrum
SIAM Journal on Computing
Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Randomly Fallible Teachers: Learning Monotone DNF with an Incomplete Membership Oracle
Machine Learning - Special issue on computational learning theory
An introduction to computational learning theory
An introduction to computational learning theory
Algorithmic complexity in coding theory and the minimum distance problem
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
Noise-tolerant learning, the parity problem, and the statistical query model
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Machine Learning
Machine Learning
Machine Learning
A Note on Learning DNF Formulas Using Equivalence and Incomplete Membership Queries
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
Learning with Queries Corrupted by Classification Noise
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Learning monotone dnf from a teacher that almost does not answer membership queries
The Journal of Machine Learning Research
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
New Results for Learning Noisy Parities and Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Attribute-Efficient and Non-adaptive Learning of Parities and DNF Expressions
The Journal of Machine Learning Research
On the inherent intractability of certain coding problems (Corresp.)
IEEE Transactions on Information Theory
Learning first-order definite theories via object-based queries
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
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We study the power of two models of faulty teachers in Valiant's PAC learning model and Angluin's exact learning model. The first model we consider is learning from an incomplete membership oracle introduced by Angluin and Slonim [D. Angluin, D.K. Slonim, Randomly fallible teachers: Learning monotone DNF with an incomplete membership oracle, Machine Learning 14 (1) (1994) 7-26]. In this model, the answers to a random subset of the learner's membership queries may be missing. The second model we consider is random persistent classification noise in membership queries introduced by Goldman, Kearns and Schapire [S. Goldman, M. Kearns, R. Schapire, Exact identification of read-once formulas using fixed points of amplification functions, SIAM Journal on Computing 22 (4) (1993) 705-726]. In this model, the answers to a random subset of the learner's membership queries are flipped. We show that in both the PAC and the exact learning models the incomplete membership oracle is strictly stronger than the noisy membership oracle under the assumption that the problem of PAC learning parities with random classification noise is intractable. We also show that under the standard cryptographic assumptions the incomplete membership oracle is strictly weaker than the perfect membership oracle. This generalizes the result of Simon [H. Simon, How many missing answers can be tolerated by query learners? Theory of Computing Systems 37 (1) (2004) 77-94] and resolves an open question of Bshouty and Eiron [N. Bshouty, N. Eiron, Learning monotone DNF from a teacher that almost does not answer membership queries, Journal of Machine Learning Research 3 (2002) 49-57].