Local learning by sparse radial basis functions

The use of radial basis functions in supervised learning is well motivated by approximation theory. Computation issues have lead us to consider some approximations of this scheme, losing much of the mathematical foundation in the process. We show that basis pursuit denoising is a principled alternative to classical RBF, which leads to sparse expansions. This alternative is local in the sense that complexity is tuned locally. A further step in this direction is made by adapting the locality parameter of each basis function. The algorithm proposed to solve this problem is simple, and the resulting solution, although extremely flexible, is governed by a single hyperparameter