COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Selective Sampling Using the Query by Committee Algorithm
Machine Learning
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
AI Game Programming Wisdom
Query by committee, linear separation and random walks
Theoretical Computer Science
Support vector machine active learning with applications to text classification
The Journal of Machine Learning Research
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Hyperplane margin classifiers on the multinomial manifold
ICML '04 Proceedings of the twenty-first international conference on Machine learning
ICML '06 Proceedings of the 23rd international conference on Machine learning
Mercer’s theorem, feature maps, and smoothing
COLT'06 Proceedings of the 19th annual conference on Learning Theory
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We introduce a computationally feasible, "constructive" active learning method for binary classification. The learning algorithm is initially formulated for separable classification problems, for a hyperspherical data space with constant data density, and for great spheres as classifiers. In order to reduce computational complexity the version space is restricted to spherical simplices and learning procedes by subdividing the edges of maximal length. We show that this procedure optimally reduces a tight upper bound on the generalization error. The method is then extended to other separable classification problems using products of spheres as data spaces and isometries induced by charts of the sphere. An upper bound is provided for the probability of disagreement between classifiers (hence the generalization error) for non-constant data densities on the sphere. The emphasis of this work lies on providing mathematically exact performance estimates for active learning strategies.