A Difference of Convex Functions Algorithm for Switched Linear Regression

Tao Pham Dinh (1) , Hoai Minh Le (2) , Hoai An Le Thi (2) , Fabien Lauer (3)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie
2 LITA - Laboratoire d'Informatique Théorique et Appliquée
3 ABC - Machine Learning and Computational Biology

This paper deals with switched linear system identification and more particularly aims at solving switched linear regression problems in a large-scale setting with both numerous data and many parameters to learn. We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The paper proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.

Mots clés: DCA; Switched linear systems; Piecewise affine systems; System identification; Switched regression; Nonconvex optimization; Nonsmooth optimization; DC programming

Domaines: Apprentissage [cs.LG]; Optimisation et contrôle [math.OC]; Automatique / Robotique

Tao Pham Dinh, Hoai Minh Le, Hoai An Le Thi, Fabien Lauer. A Difference of Convex Functions Algorithm for Switched Linear Regression. IEEE Transactions on Automatic Control, 2014, ⟨10.1109/TAC.2014.2301575⟩. ⟨hal-00931206⟩