A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Training connectionist networks with queries and selective sampling
Advances in neural information processing systems 2
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Bounds on the Sample Complexity of Bayesian Learning Using Information Theory and the VC Dimension
Machine Learning - Special issue on computational learning theory
Selective Sampling Using the Query by Committee Algorithm
Machine Learning
A PAC analysis of a Bayesian estimator
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Query by Committee, Linear Separation and Random Walks
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Query by Committee, Linear Separation and Random Walks
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
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Recent works have shown the advantage of using Active Learning methods, such as the Query by Committee (QBC) algorithm, to various learning problems. This class of Algorithms requires an oracle with the ability to randomly select a consistent hypothesis according to some predefined distribution. When trying to implement such an oracle, for the linear separators family of hypotheses, various problems should be solved. The major problem is time-complexity, where the straight-forward Monte Carlo method takes exponential time. In this paper we address some of those problems and show how to convert them to the problems of sampling from convex bodies or approximating the volume of such bodies. We show that recent algorithms for approximating the volume of convex bodies and approximately uniformly sampling from convex bodies using random walks, can be used to solve this problem, and yield an efficient implementation for the QBC algorithm. This solution suggests a connection between random walks and certain properties known in machine learning such as ∈-net and support vector machines. Working out this connection is left for future work.