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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Veröffentlicht in:IEEE transactions on automatic control Jg. 59; H. 8; S. 2277 - 2282
Hauptverfasser: Tao Pham Dinh, Hoai Minh Le, Hoai An Le Thi, Lauer, Fabien
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.08.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Schlagworte:
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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Beschreibung
Zusammenfassung: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2014.2301575