A Difference of Convex Functions Algorithm for Switched Linear Regression
Identifieur interne : 000D84 ( Main/Merge ); précédent : 000D83; suivant : 000D85A Difference of Convex Functions Algorithm for Switched Linear Regression
Auteurs : Tao Pham Dinh [France] ; Hoai Minh Le [France] ; Hoai An Le Thi [France] ; Fabien Lauer [France]Source :
- IEEE Transactions on Automatic Control [ 0018-9286 ] ; 2014.
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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.
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DOI: 10.1109/TAC.2014.2301575
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<front><div type="abstract" xml:lang="en">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.</div>
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