Communications of the ACM
Learning decision trees using the Fourier spectrum
SIAM Journal on Computing
SIAM Journal on Computing
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Learning DNF over the Uniform Distribution Using a Quantum Example Oracle
SIAM Journal on Computing
Theoretical Advances in Neural Computation and Learning
Theoretical Advances in Neural Computation and Learning
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Equivalences and Separations Between Quantum and Classical Learnability
SIAM Journal on Computing
A lower bound for testing juntas
Information Processing Letters
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
The geometry of quantum learning
Quantum Information Processing
Quantum complexity of testing group commutativity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Learning juntas in the presence of noise
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Improved Bounds for Testing Juntas
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
Application of a generalization of russo's formula to learning from multiple random oracles
Combinatorics, Probability and Computing
Quantum algorithms for highly non-linear Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Testing juntas: a brief survey
Property testing
Testing juntas: a brief survey
Property testing
Quantum algorithms for shifted subset problems
Quantum Information & Computation
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization
Journal of the ACM (JACM)
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In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: (1) whose sample complexity has no dependence on n, the dimension of the domain the Boolean functions are defined over; (2) with no access to any classical or quantum membership ("black-box") queries. Instead, our algorithms use only classical examples generated uniformly at random and fixed quantum superpositions of such classical examples; (3) which require only a few quantum examples but possibly many classical random examples (which are considered quite "cheap" relative to quantum examples). Our quantum algorithms are based on a subroutine FS which enables sampling according to the Fourier spectrum of f; the FS subroutine was used in earlier work of Bshouty and Jackson on quantum learning. Our results are as follows: (1) We give an algorithm for testing k-juntas to accuracy 驴 that uses O(k/驴) quantum examples. This improves on the number of examples used by the best known classical algorithm. (2) We establish the following lower bound: any FS-based k-junta testing algorithm requires $$\Omega(\sqrt{k})$$ queries. (3) We give an algorithm for learning k-juntas to accuracy 驴 that uses O(驴驴1 k log k) quantum examples and O(2 k log(1/驴)) random examples. We show that this learning algorithm is close to optimal by giving a related lower bound.