On Learning Simple Deterministic and Probabilistic Neural Concepts

We investigate the learnability, under the uniform distribution, of deterministic and probabilistic neural concepts that can be represented as simple combinations of nonoverlapping perceptrons with binary weights. Two perceptrons are said to be nonoverlapping if they do not share any input variables. In the deterministic case, we investigate, within the distribution-specific PAC model, the learnability of perceptron decision lists and generalized perceptron decision lists. In the probabilistic case, we adopt the approach of learning with a model of probability introduced by Kearns and Schapire [10] and Yamanishi [14], and investigate a class of concepts we call probabilistic majorities of nonoverlapping perceptrons. We give polynomial time algorithms for learning these restricted classes of networks. The algorithms work by estimating various statistical quantities that yield enough information to infer, with high probability, the target concept.