Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
The statistical theory of linear systems
The statistical theory of linear systems
System identification
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
A Geometric Approach to the Minimum Sensitivity Design Problem
SIAM Journal on Control and Optimization
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Survey Generic properties and control of linear structured systems: a survey
Automatica (Journal of IFAC)
Asymptotic properties of subspace estimators
Automatica (Journal of IFAC)
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
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In this paper a novel method is presented for the identification of sparse dynamical interaction networks, such as gene regulatory networks. This method uses mixed L2/L1 minimization: nonlinear least squares optimization to achieve an optimal fit between the model in state space form and the data, and L1-minimization of the parameter vector to find the sparsest such model possible. In this approach, in contrast to previous research, the dynamical aspects of the model are taken into account, which gives rise to a nonlinear estimation problem. The setup allows for the identification of structured or partially sparse models, so that available prior knowledge on interactions can be incorporated. To investigate the potential for applications, the algorithm is tested on artificial gene regulatory networks.