Régression linéaire au sens des moindres carrés à partir de sous-espaces vectoriels aléatoires

Exposé en français mais transparents en anglais
 
I will present recent works on least-squares regression using randomly generated subspaces.In this approach, the regression function is the empirical risk minimizer in a low dimensional randomly generated subspace of a high (possibly infinite) dimensional function space. This approach can be seen as an alternative to usual penalization techniques. Approximation error and excess risk bounds are derived and the issue of numerical complexity will be discussed.This is joint work with Odalric Maillard and is described in the following papers:
– Compressed Least-Squares Regression, NIPS 2009
– Brownian Motions and Scrambled Wavelets for Least-Squares Regression, NIPS 2010