French
English
We propose a principled framework for learning with infi nitely many features, situations that are usually induced by continuously parametrized feature extraction methods. Such cases occur for instance when considering Gabor-based features in computer vision problems or when dealing with Fourier features for kernel approximations. We cast the problem as the one of fi nding a fi nite subset of features that minimizes a regularized empirical risk. After having analyzed the optimality conditions of such a problem, we propose a simple algorithm which has the flavour of a column-generation technique. We also show that using Fourier-based features, it is possible to perform approximate infi nite kernel learning. Our experimental results on several datasets show the bene fits of the proposed approach in several situations including texture classi cation, pixel classification and large-scale kernelized problems (involving about 100 thousand examples).