Risk minimization in impulse response estimation

主讲人:Hakan Hjalmarsson (Kungliga Tekniska hogskolan)
时间:2015年10月22日上午9:00   地点:N514


The use of new kernels, e.g. the stable spline kernel, in combination with the Empirical Bayes (EB) approach has lead to very potent algorithms for estimating dynamical systems. In this talk we take a frequentistic approach and consider the problem  of determining the so called hyperparameters  from a Mean Square Error perspective. This leads to a framework where first the rank-1 matrix obtained by squaring (in a matrix sense)  the impulse response  of the system has to be estimated from data, and then the hyperparameters are found by minimizing an estimate of  the MSE.  We show that a range of existing methods can be interpreted as different approaches to estimate the rank-1 matrix, e.g.  Stein's Unbiased Risk Estimate as well as the aforementioned EB approach.  This framework also allows us to show that when the kernel itself is rank-1 and linearly parametrized, the EB-approach leads to an estimator of James-Stein type, i.e. a shrinkage estimator. 



H?kan Hjalmarsson is Professor at the School of Electrical Engineering, KTH, Stockholm, Sweden. He is an IEEE Fellow and Chair of the IFAC Coordinating Committee on Systems and Signals. He has held visiting research positions at California Institute of Technology, Louvain University and at the University of Newcastle, Australia.  His research interests include system identification, signal processing, control and estimation in communication networks and automated tuning of controllers.