Using domain-specific knowledge in generalization error bounds for support vector machine learning

In this study we describe a methodology to exploit a specific type of domain knowledge in order to find tighter error bounds on the performance of classification via Support Vector Machines. The domain knowledge we consider is that the input space lies inside of a specified convex polytope. First, we consider prior knowledge about the domain by incorporating upper and lower bounds of attributes. We then consider a more general framework that allows us to encode prior knowledge in the form of linear constraints formed by attributes. By using the ellipsoid method from optimization literature, we show that, this can be exploited to upper bound the radius of the hyper-sphere that contains the input space, and enables us to tighten generalization error bounds. We provide a comparative numerical analysis and show the effectiveness of our approach.