Hardness of approximate two-level logic minimization and PAC learning with membership queries
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Polynomial certificates for propositional classes
Information and Computation
Eulogy: Michael (Misha) Alekhnovich 1978-2006
ACM SIGACT News
Unconditional lower bounds for learning intersections of halfspaces
Machine Learning
DNF are teachable in the average case
Machine Learning
Projective DNF formulae and their revision
Discrete Applied Mathematics
On hardness of learning intersection of two halfspaces
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximating Optimal Binary Decision Trees
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Efficient learning algorithms yield circuit lower bounds
Journal of Computer and System Sciences
Cryptographic hardness for learning intersections of halfspaces
Journal of Computer and System Sciences
Polynomial certificates for propositional classes
Information and Computation
SIAM Journal on Computing
DNF are teachable in the average case
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Improved lower bounds for learning intersections of halfspaces
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Efficient learning algorithms yield circuit lower bounds
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Complexity of propositional proofs
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Activized learning: transforming passive to active with improved label complexity
The Journal of Machine Learning Research
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We consider the complexity of properly learning concept classes, i.e. when the learner must output a hypothesis of the same form as the unknown concept. We present the following new upper and lower bounds on well-known concept classes: We show that unless NP = RP, there is no polynomial-time PA Clearning algorithm for DNF formulae where the hypothesis is an OR-of-thresholds. Note that as special cases, we show that neither DNF nor OR-of-thresholds are properly learnable unless NP = RP. Previous hardness results have required strong restrictions on the size of the output DNF formula. We also prove that it is NP-hard to learn the intersection of \ell\geqslant 2 halfspaces by the intersection of k halfspaces for any constant k 驴 0. Previous work held for the case when k = \ell. Assuming that NP 驴 DTIME(2^{n^\varepsilon} ) for a certain constant 驴