Interpolation and approximation of sparse multivariate polynomials over GF(2)
SIAM Journal on Computing
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Learning hierarchical rule sets
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Learning Boolean Functions in an Infinite Attribute Space
Machine Learning
Edge search in graphs and hypergraphs of bounded rank
Discrete Mathematics
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Learning Boolean concepts in the presence of many irrelevant features
Artificial Intelligence
A tight upper bound for group testing in graphs
Discrete Applied Mathematics
The Power of Self-Directed Learning
Machine Learning
Learning in the presence of finitely or infinitely many irrelevant attributes
Journal of Computer and System Sciences
Randomized algorithms
Exact learning Boolean functions via the monotone theory
Information and Computation
A group testing problem for hypergraphs of bounded rank
Discrete Applied Mathematics
Optimal pooling designs with error detection
Journal of Combinatorial Theory Series A
Attribute-efficient learning in query and mistake-bound models
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
Artificial Intelligence
Online Learning versus Offline Learning
Machine Learning
The query complexity of finding local minima in the lattice
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Randomized group testing for mutually obscuring defectives
Information Processing Letters
Improved algorithms for group testing with inhibitors
Information Processing Letters
On the cut-off point for combinatorial group testing
Discrete Applied Mathematics
Lower bounds for identifying subset members with subset queries
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Machine Learning
Machine Learning
A Chip Search Problem on Binary Numbers
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Optimal Attribute-Efficient Learning of Disjunction, Parity and Threshold Functions
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
The Algorithmic Complexity of Chemical Threshold Testing
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Group Testing Problems with Sequences in Experimental Molecular Biology
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Approximate Location of Relevant Variables under the Crossover Distribution
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
On parallel attribute-efficient learning
Journal of Computer and System Sciences
Theory revision with queries: horn, read-once, and parity formulas
Artificial Intelligence
Exploiting Product Distributions to Identify Relevant Variables of Correlation Immune Functions
The Journal of Machine Learning Research
General Theory of Information Transfer and Combinatorics
Strengthening hash families and compressive sensing
Journal of Discrete Algorithms
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We study the complexity of learning arbitrary Boolean functions of n variables by membership queries, if at most r variables are relevant. Problems of this type have important applications in fault searching, e.g. logical circuit testing and generalized group testing. Previous literature concentrates on special classes of such Boolean functions and considers only adaptive strategies. First we give a straightforward adaptive algorithm using O(r2r log n) queries, but actually, most queries are asked nonadaptively. This leads to the problem of purely nonadaptive learning. We give a graph-theoretic characterization of nonadaptive learning families, called r-wise bipartite connected families. By the probabilistic method we show the existence of such families of size O(r2r log n + r22r). This implies that nonadaptive attribute-efficient learning is not essentially more expensive than adaptive learning. We also sketch an explicit pseudopolynomial construction, though with a slightly worse bound. It uses the common derandomization technique of small-biased k-independent sample spaces. For the special case r = 2, we get roughly 2.275 log n adaptive queries, which is fairly close to the obvious lower bound of 2 log n. For the class of monotone functions, we prove that the optimal query number O(2r + r log n) can be already achieved in O(r) stages. On the other hand, Ω(2r log n) is a lower bound on nonadaptive queries.