Lower bounds for PAC learning with queries
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
An introduction to computational learning theory
An introduction to computational learning theory
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing Basic Boolean Formulae
SIAM Journal on Discrete Mathematics
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
A lower bound for distribution-free monotonicity testing
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Distribution-free testing algorithms for monomials with a sublinear number of queries
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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In the distribution-freeproperty testing model, the distance between functions is measured with respect to an arbitrary and unknown probability distribution $\mathcal{D}$ over the input domain. We consider distribution-free testing of several basic Boolean function classes over {0,1}n, namely monotone conjunctions, general conjunctions, decision lists, and linear threshold functions. We prove that for each of these function classes, 茂戮驴((n/logn)1/5) oracle calls are required for any distribution-free testing algorithm. Since each of these function classes is known to be distribution-free properly learnable (and hence testable) using 茂戮驴(n) oracle calls, our lower bounds are within a polynomial factor of the best possible.