Multi-output learning via spectral filtering

In this paper we study a class of regularized kernel methods for multi-output learning which are based on filtering the spectrum of the kernel matrix. The considered methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector-valued extensions of L2 boosting and other iterative schemes. Computational properties are discussed for various examples of kernels for vector-valued functions and the benefits of iterative techniques are illustrated. Generalizing previous results for the scalar case, we show a finite sample bound for the excess risk of the obtained estimator, which allows to prove consistency both for regression and multi-category classification. Finally, we present some promising results of the proposed algorithms on artificial and real data.