A Study of Maximal-Coverage Learning Algorithms

The coverage of a learning algorithm is the number of concepts that can be learned by that algorithm from samples of a given size. This paper asks whether good learning algorithms can be designed by maximizing their coverage. The paper extends a previous upper bound on the coverage of any Boolean concept learning algorithm and describes two algorithms|Multi-Balls and Large-Ball|whose coverage approaches this upper bound. Experimental measurement of the coverage of the ID3 and FRINGE algorithms shows that their coverage is far below this bound. Further analysis of Large-Ball shows that although it learns many concepts, these do not seem to be very interesting concepts. Hence, coverage maximization alone does not appear to yield practically-useful learning algorithms. The paper concludes with a deenition of coverage within a bias, which suggests a way that coverage maximization could be applied to strengthen weak preference biases.