Binarsity: a penalization for one-hot encoded features

This paper deals with the problem of large-scale linear supervised learning in settings where a large number of continuous features are available. We propose to combine the well-known trick of one-hot encoding of continuous features with a new penalization called binarsity. In each group of binary features coming from the one-hot encoding of a single raw continuous feature, this penalization uses total-variation regularization together with an extra linear constraint to avoid collinearity within groups. Non-asymptotic oracle inequalities for generalized linear models are proposed, and numerical experiments illustrate the good performances of our approach on several datasets. It is also noteworthy that our method has a numerical complexity comparable to standard $\ell_1$ penalization.