A Difference of Convex Functions Algorithm for Switched Linear Regression

This technical note 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 functi...

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Vydáno v:	IEEE transactions on automatic control Ročník 59; číslo 8; s. 2277 - 2282
Hlavní autoři:	Tao Pham Dinh, Hoai Minh Le, Hoai An Le Thi, Lauer, Fabien
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.08.2014 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Témata:	Algorithms Automatic Computational efficiency Computational modeling Computer Science Convergence Data models Data points DC programming DCA Direct current Engineering Sciences Linear systems Machine Learning Mathematical analysis Mathematical models Mathematics nonconvex optimization nonsmooth optimization Optimization Optimization and Control piecewise affine systems Programming Regression switched linear systems switched regression Switches system identification Vectors Switched linear systems Nonconvex optimization DCA Piecewise affine systems Switched regression DC programming Nonsmooth optimization System identification
ISSN:	0018-9286, 1558-2523
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Abstract	This technical note 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 technical note 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.
AbstractList	This technical note 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 technical note 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. 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.
Author	Hoai An Le Thi Lauer, Fabien Hoai Minh Le Tao Pham Dinh
Author_xml	– sequence: 1 surname: Tao Pham Dinh fullname: Tao Pham Dinh organization: Lab. of Math., Normandie Univ., St.-Etienne-du-Rouvray, France – sequence: 2 surname: Hoai Minh Le fullname: Hoai Minh Le organization: LORIA, Univ. de Lorraine, Vandœuvre-lès-Nancy, France – sequence: 3 surname: Hoai An Le Thi fullname: Hoai An Le Thi organization: LORIA, Univ. de Lorraine, Vandœuvre-lès-Nancy, France – sequence: 4 givenname: Fabien surname: Lauer fullname: Lauer, Fabien organization: Lab. of Theor. & Appl. Comput. Sci., Univ. of Lorraine, Metz, France
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SubjectTerms	Algorithms Automatic Computational efficiency Computational modeling Computer Science Convergence Data models Data points DC programming DCA Direct current Engineering Sciences Linear systems Machine Learning Mathematical analysis Mathematical models Mathematics nonconvex optimization nonsmooth optimization Optimization Optimization and Control piecewise affine systems Programming Regression switched linear systems switched regression Switches system identification Vectors
Title	A Difference of Convex Functions Algorithm for Switched Linear Regression
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