Dual-to-kernel learning with ideals

In this paper, we propose a learning theory which is the synthesis of kernel and symbolic algebraic methods, by exposing inherent dualities between them. We use this duality to combine the structure-awareness of algebraic methods with the efficiency and generality of kernels. Since their invention by Boser, Guyon and Vapnik [2, 22], kernel methods have had a fundamental impact on the fields of statistics and machine learning. The major appeal of using kernel methods for learning consists in using the kernel trick, first proposed by Aizerman, Braverman and Rozonoer [1], which allows to make otherwise costly computations in the feature space implicit and thus highly efficient for a huge variety of learning tasks - see e.g.