Efficiently Learning Monotone Decision Trees with ID3

Since the Probably Approximately Correct learning model was introduced in 1984, there has been much effort in designing computationally efficient algorithms for learning Boolean functions from random examples drawn from a uniform distribution. In this paper, I take the ID3 information-gain-first classification algorithm and apply it to the task of learning monotone Boolean functions from examples that are uniformly distributed over {0,1}^n. I limited my scope to the class of monotone Boolean functions that can be represented as read-2 width-2 disjunctive normal form expressions. I modeled these functions as graphs and examined each type of connected component contained in these models, i.e. path graphs and cycle graphs. I determined the influence of the variables in the pieces of these graph models in order to understand how ID3 behaves when learning these functions. My findings show that ID3 will produce an optimal decision tree for this class of Boolean functions

On PAC learning algorithms for rich Boolean function classes

We give an overview of the fastest known algorithms for learning various expressive classes of Boolean functions in the Probably Approximately Correct (PAC) learning model. In addition to surveying previously known results, we use existing techniques to give the first known subexponential-time algorithms for PAC learning two natural and expressive classes of Boolean functions: sparse polynomial threshold functions over the Boolean cube {0, 1}^n and sparse GF2 polynomials over {0, 1}^n