Communications of the ACM
Learning decision trees using the Fourier spectrum
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fast learning of k-term DNF formulas with queries
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An introduction to computational learning theory
An introduction to computational learning theory
Exact learning Boolean functions via the monotone theory
Information and Computation
Asking questions to minimize errors
Journal of Computer and System Sciences
Simple learning algorithms using divide and conquer
Computational Complexity
A simple algorithm for learning O (log n)-term DNF
Information Processing Letters
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
Automatic Construction of Decision Trees from Data: A Multi-Disciplinary Survey
Data Mining and Knowledge Discovery
Exact learning of DNF formulas using DNF hypotheses
Journal of Computer and System Sciences - Special issue on COLT 2002
Comprehensive Functional Verification: The Complete Industry Cycle (Systems on Silicon)
Comprehensive Functional Verification: The Complete Industry Cycle (Systems on Silicon)
Attribute-Efficient and Non-adaptive Learning of Parities and DNF Expressions
The Journal of Machine Learning Research
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Learning nested halfspaces and uphill decision trees
COLT'07 Proceedings of the 20th annual conference on Learning theory
Active sampling for multiple output identification
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Parameterized Complexity
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In this paper we investigate the problem of active learning the partition of the n-dimensional hypercube into mcubes, where the i-th cube has color i. The model we are using is exactlearning via color evaluation queries, without equivalence queries, as proposed by the work of Fine and Mansour. We give a randomized algorithm solving this problem in O(mlogn) expected number of queries, which is tight, while its expected running time is O(m2nlogn).Furthermore, we generalize the problem to allow partitions of the cube into mmonochromatic parts, where each part is the union of pcubes. We give two randomized algorithms for the generalized problem. The first uses O(mp22plogn) expected number of queries, which is almost tight with the lower bound. However, its naïve implementation requires an exponential running time in n. The second, more practical, algorithm achieves a better running time complexity of $\tilde{O}(m^2 n^2 2^{2^p})$. However, it may fail to learn the correct partition with an arbitrarily small probability and it requires slightly more expected number of queries: $\tilde{O}(mn 4^p)$, where the $\tilde{O}$ represents a poly logarithmic factor in m,n,2p.