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.
Publié le : 2014-07-04
Classification:
Nonsmooth optimization,
Nonconvex optimization,
System identification,
Switched regression,
Switched linear systems,
Piecewise affine systems,
DC programming,
DCA,
[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG],
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC],
[SPI.AUTO]Engineering Sciences [physics]/Automatic
@article{hal-00931206,
author = {Pham Dinh, Tao and Le, Hoai Minh and Le Thi, Hoai An and Lauer, Fabien},
title = {A Difference of Convex Functions Algorithm for Switched Linear Regression},
journal = {HAL},
volume = {2014},
number = {0},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00931206}
}
Pham Dinh, Tao; Le, Hoai Minh; Le Thi, Hoai An; Lauer, Fabien. A Difference of Convex Functions Algorithm for Switched Linear Regression. HAL, Tome 2014 (2014) no. 0, . http://gdmltest.u-ga.fr/item/hal-00931206/