T. Pham Dinh, H.M. Le, H.A. Le Thi, F. Lauer, A Difference of Convex Functions Algorithm for Switched Linear Regression.

Abstract: 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.


Keywords: Switched linear systems, Piecewise affine systems, System identification, Switched regression, Nonconvex optimization, Nonsmooth optimization, DC programming, DCA.


Citation: 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, Volume 59, Issue 8, pp. 2277-2282, August 2014.


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