Learning smooth models of nonsmooth functions via convex optimization

Fabien Lauer (1) , van Luong Le (2) , Gérard Bloch (2)

1 ABC - Machine Learning and Computational Biology
2 CRAN - Centre de Recherche en Automatique de Nancy

This paper proposes a learning framework and a set of algorithms for nonsmooth regression, i.e., for learning piecewise smooth target functions with discontinuities in the function itself or the derivatives at unknown locations. In the proposed approach, the model belongs to a class of smooth functions. Though constrained to be globally smooth, the trained model can have very large derivatives at particular locations to approximate the nonsmoothness of the target function. This is obtained through the definition of new regularization terms which penalize the derivatives in a location-dependent manner and training algorithms in the form of convex optimization problems. Examples of application to hybrid dynamical system identification and image reconstruction are provided.

Domaines: Apprentissage [cs.LG]

Fabien Lauer, van Luong Le, Gérard Bloch. Learning smooth models of nonsmooth functions via convex optimization. 22nd International Workshop on Machine Learning for Signal Processing, IEEE-MLSP 2012, Sep 2012, Santander, Spain. pp.CDROM. ⟨hal-00719188⟩