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 in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Fast Approximate PCPs for Multidimensional Bin-Packing Problems
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
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 '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Three Theorems Regarding Testing Graph Properties
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the strength of comparisons in property testing
Information and Computation
Testing monotonicity over graph products
Random Structures & Algorithms
Distribution-Free Testing Lower Bounds for Basic Boolean Functions
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
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
Hi-index | 0.00 |
We consider monotonicity testing of functions f:[n]d→ {0,1}, in the property testing framework of Rubinfeld and Sudan [23] and Goldreich, Goldwasser and Ron [14]. Specifically, we consider the framework of distribution-free property testing, where the distance between functions is measured with respect to a fixed but unknown distribution D on the domain and the testing algorithms have an oracle access to random sampling from the domain according to this distribution D. We show that, though in the uniform distribution case, testing of boolean functions defined over the boolean hypercube can be done using query complexity that is polynomial in $\frac{1}{\epsilon}$ and in the dimension d, in the distribution-free setting such testing requires a number of queries that is exponential in d. Therefore, in the high-dimensional case (in oppose to the low-dimensional case), the gap between the query complexity for the uniform and the distribution-free settings is exponential.