Generalized RBF kernel for incomplete data

Abstract

We construct genRBF kernel, which generalizes standard Gaussian RBF kernel to the case of incomplete data. Instead of using typical imputation techniques, which fill missing attributes by single values, we model possible outcomes at missing coordinates using data distribution. This allows to derive analytical formula for the expected value of RBF kernel taken over all possible imputations, which is a basic idea behind our method. In particular, for complete observations genRBF reduces to standard RBF kernel. Experiments show that introduced kernel applied to SVM classifier and regressor gives better results than state-of-the-art methods, especially in the case when large number of features is missing. Moreover, genRBF is easy to implement and can be used together with any kernel approach without any additional modifications.