Generalization error bounds for the logical analysis of data

This paper analyses the predictive performance of standard techniques for the `logical analysis of data' (LAD), within a probabilistic framework. Improving and extending earlier results, we bound the generalization error of classifiers produced by standard LAD methods in terms of their complexity and how well they fit the training data. We also obtain bounds on the predictive accuracy which depend on the extent to which the underlying LAD discriminant function achieves a large separation (a `large margin') between (most of) the positive and negative observations.