Communications of the ACM
Computational limitations on learning from examples
Journal of the ACM (JACM)
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Composite geometric concepts and polynomial predictability
COLT '90 Proceedings of the third annual workshop on Computational learning theory
Fast learning of k-term DNF formulas with queries
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On-line learning of rectangles
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Lower Bound Methods and Separation Results for On-Line Learning Models
Machine Learning - Computational learning theory
Learning unions of two rectangles in the plane with equivalence queries
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
On-line learning of rectangles in noisy environments
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Learning from a consistently ignorant teacher
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Machine Learning
Machine Learning
Learning from a consistently ignorant teacher
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
DNF—if you can't learn'em, teach'em: an interactive model of teaching
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Noise-tolerant parallel learning of geometric concepts
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
Intrinsic Complexity of Learning Geometrical Concepts from Positive Data
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Intrinsic complexity of learning geometrical concepts from positive data
Journal of Computer and System Sciences
Learning unions of ω(1)-dimensional rectangles
Theoretical Computer Science
Active learning with multiple views
Journal of Artificial Intelligence Research
Learning unions of ω(1)-dimensional rectangles
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
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We present two algorithms that use membership and equivalence queries to exactly identify the concepts given by the union of s discretized axis-parallel boxes in d-dimensional discretized Euclidean space where there are n discrete values that each coordinate can have. The first algorithm receives at most sd counterexamples and uses time and membership queries polynomial in s and logn for any d constant. Further, all equivalence queries made can be formulated as the union of O(sdlogs) axis parallel boxes.Next, we introduce a new complexity measure that better captures the complexity of a union of boxes than simply the number of boxes and dimensions. Our new measure, &sgr;, is the number of segments in the target polyhedron where a segment is a maximum portion of one of the sides of the polyhedron that lies entirely inside or entirely outside each of the other halfspaces defining the polyhedron. We then present an improvement of our first algorithm that uses time and queries polynomial in &sgr; and logn. The hypothesis class used here is decision trees of height at most 2sd. Further we can show that the time and queries used by this algorithm are polynomial in d and logn for s any constant thus generating the exact learnability of DNF formulas with a constant number of terms. In fact, this single algorithm is efficient for either s or d constant.