Peeters, Ralf (Univ. Maastricht), Tossings, Ivo (Univ. Maastricht), Zeemering, Stef (Univ. Maastricht)

Sparse System Identification by Mixed L1/L2 Minimization

Scheduled for presentation during the Regular Session "Linear System Identification III" (WeA09), Wednesday, July 26, 2006, 12:05−12:30, Room J

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 22, 2024

Abstract

In this paper an approach to sparse system identification is advocated which employs an L2-norm to optimize the fit between a model and the data (using a conventional least squares criterion with respect to the vector of prediction errors) and an L1-norm to minimize the size of the parameter vector to achieve model sparsity. The set of models under consideration is that of state space models in innovations form, using either a full parameterization, data-driven local coordinates (DDLC) or a structured parameterization. The sparse system identification procedure allows one to deal with identifiability problems and parameter redundancy, for instance due to a very limited amount of available measurement data. The approach is motivated by applications in the area of reverse engineering of gene regulatory networks and inspired by a similar technique described in a static linear setting in the literature. In the current approach, the dynamical aspects are properly taken into account, in contrast to previous work where simplifications are made to arrive at a linear estimation problem.

Computation of search directions for L1-norm optimization can be performed effectively and fast, as this involves the solution of an LP problem. The same holds for numerical optimization of the nonlinear least squares criterion with a Gauss-Newton type iterative local search method. There are however some convergence issues to be dealt with when the two optimization problems are combined. The sparse estimation method is applicable to structured models where only a selected subset of entries from the system matrices (A,B,C,D,K) requires estimation.