Binarsity: a penalization for one-hot encoded features in linear supervised learning

Mokhtar Z. Alaya; Simon Bussy; Stéphane Gaïffas; Agathe Guilloux

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arXiv · 1703.08619

Binarsity: a penalization for one-hot encoded features in linear supervised learning

Mokhtar Z. Alaya·Simon Bussy·Stéphane Gaïffas·Agathe Guilloux

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Abstract

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 \emph{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. This induces two interesting properties on the model weights of the one-hot encoded features: they are piecewise constant, and are eventually block sparse. Non-asymptotic oracle inequalities for generalized linear models are proposed. Moreover, under a sparse additive model assumption, we prove that our procedure matches the state-of-the-art in this setting. 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.

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BibTeX RIS

Mokhtar Z. Alaya, Simon Bussy, Stéphane Gaïffas, Agathe Guilloux. 2019-01-09. Binarsity: a penalization for one-hot encoded features in linear supervised learning. https://arxiv.org/abs/1703.08619

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