Regularization for efficient bias-variance trade-off is a well known tool in statistics. Careful choice and tuning of the regularization matrix has been of central recent interest also for methods to estimate a system's impulse response in system identification. We discuss in this talk the use of regularization matrices that are formed as linear combinations of preselected matrices. We show the potential advantages of such regularization for systems with widely spread time constants, and make comparisons over large data banks of complex systems. Estimating the best weights of the preselected matrices is not a convex problem, but we show how convex programming techniques can be used for effective numerical implementations of the tuning. The talk is based on joint work with Tianshi Chen, Martin Andersen, Alessandro Chiuso and Gianluigi Pillonetto.
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