Generalization bounds for weighted binary classification with applications to statistical verification

We describe an approach to statistically verifying complex controllers. This approach is based on deriving practical Vapnik-Chervonenkis-style (VC) generalization bounds for binary classifiers with weighted loss. An important case is deriving bounds on the probability of false positive. We show how existing methods to derive bounds on classification error can be extended to derive similar bounds on the probability of false positive, as well as bounds in a decision-theoretic setting that allows tradeoffs between false negatives and false positives. We describe experiments using these bounds in statistically verifying computational properties of an iterative controller for an Organic Air Vehicle (OAV).