Selection of relevant features and examples in machine learning
Artificial Intelligence - Special issue on relevance
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing Basic Boolean Formulae
SIAM Journal on Discrete Mathematics
Finding Relevant Variables in PAC Model with Membership Queries
ALT '99 Proceedings of the 10th International Conference on Algorithmic Learning Theory
A lower bound for testing juntas
Information Processing Letters
Journal of Computer and System Sciences - Special issue on FOCS 2002
Learning functions of k relevant variables
Journal of Computer and System Sciences - Special issue: STOC 2003
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
Testing for Concise Representations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A query efficient non-adaptive long code test with perfect completeness
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Testing juntas: a brief survey
Property testing
Testing juntas: a brief survey
Property testing
Lower bounds for testing computability by small width OBDDs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Approximating the influence of monotone boolean functions in O(√n) query complexity
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On approximating the number of relevant variables in a function
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
On Approximating the Number of Relevant Variables in a Function
ACM Transactions on Computation Theory (TOCT)
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We consider the problem of testing functions for the property of being a k-junta (i.e., of depending on at most kvariables). Fischer, Kindler, Ron, Safra, and Samorodnitsky (J. Comput. Sys. Sci., 2004) showed that $\tilde{O}(k^2)/\epsilon$ queries are sufficient to test k-juntas, and conjectured that this bound is optimal for non-adaptive testing algorithms.Our main result is a non-adaptive algorithm for testing k-juntas with $\tilde{O}(k^{3/2})/\epsilon$ queries. This algorithm disproves the conjecture of Fischer et al.We also show that the query complexity of non-adaptive algorithms for testing juntas has a lower bound of $\min \big(\tilde{\Omega}(k/\epsilon), 2^k/k\big)$, essentially improving on the previous best lower bound of 茂戮驴(k).