Collaborating Authors

Computational Learning Theory

A training algorithm for optimum margin classifiers


Proceedings of the Fifth Annual Workshop on Computational Learning Theory 5: 144-152, 1992.

The Strength of Weak Learnability


This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distribution-free (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a Source of examples of the unknown concept, the learner with high probability is able to output an hypothesis that is correct on all but an arbitrarily small fraction of the instances. The concept class is weakly learnable if the learner can produce an hypothesis that performs only slightly better than random guessing.In this paper, it is shown that these two notions of learnability are equivalent. A method is described for converting a weak learning algorithm into one that achieves arbitrarily high accuracy. This construction may have practical applications as a tool for efficiently converting a mediocre learning algorithm into one that performs extremely well. In addition, the construction has some interesting theoretical consequences, including a set of general upper bounds on the complexity of any strong learning algorithm as a function of the allowed error e.See also: SpringerLinkMachine Learning, 5 (2), 197-227

Learnability and the Vapnik-Chervonenkis dimension


Valiant’s learnability model is extended to learning classes of concepts defined by regions in Euclidean space E”. The methods in this paper lead to a unified treatment of some of Valiant’s results, along with previous results on distribution-free convergence of certain pattern recognition algorithms. It is shown that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned. Using this parameter, the complexity and closure properties of learnable classes are analyzed, and the necessary and sufftcient conditions are provided for feasible learnability.JACM, 36 (4), 929-65

Game-playing and game-learning automata


In Fox, L. (Ed.), Advances in Programming and Non-Numerical Computation, pp. 183–200. Pergamon.