Regularized spectrum estimation using stable spline kernels

Dr. Giulio Bottegal (KTH)

SYSTEMS AND CONTROL SERIES

DATE: 2013-08-16
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU
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ABSTRACT:
We present a new regularized kernel-based approach for the estimation of the second order moments of stationary stochastic processes. The proposed estimator is defined by a Tikhonov-type variational problem. It contains few unknown parameters which can be estimated by cross validation solving a sequence of problems whose computational complexity scales linearly with the number of noisy moments (derived from the samples of the process). The correlation functions are assumed to be summable and the hypothesis space is a reproducing kernel Hilbert space induced by the recently introduced stable spline kernel. In this way, information on the decay to zero of the functions to be reconstructed is incorporated in the estimation process. An application to the identification of transfer functions in the case of white noise as input is also presented. Numerical simulations show that the proposed method compares favorably with respect to standard nonparametric estimation algorithms that exploit an oracle-type tuning of the parameters.

BIO:
Giulio Bottegal received the Master degree in Automation Engineering (cum laude) in 2009 and the PhD degree in Information Engineering in 2013 from the University of Padova. Currently, he holds a position as research fellow (postdoc) at the School of Electrical Engineering, KTH Royal Institute of Technology. His research interests include stochastic systems, latent variables models, regularization techniques for system identification.