Estimation of the Forgetting Factor in Kernel Recursive Least Squares

TitleEstimation of the Forgetting Factor in Kernel Recursive Least Squares
Publication TypeConference Paper
Year of Publication2012
AuthorsS. Van Vaerenbergh, I. Santamaría, and M. Lázaro-Gredilla
Conference Name2012 IEEE International Workshop On Machine Learning For Signal Processing (MLSP)
Month PublishedSeptember
Keywordskernel adaptive filtering
AbstractIn a recent work we proposed a kernel recursive least-squares tracker (KRLS-T) algorithm that is capable of tracking in non-stationary environments, thanks to a forgetting mechanism built on a Bayesian framework. In order to guarantee optimal performance its parameters need to be determined, specifically its kernel parameters, regularization and, most importantly in non-stationary environments, its forgetting factor. This is a common difficulty in adaptive filtering techniques and in signal processing algorithms in general. In this paper we demonstrate the equivalence between KRLS-T’s recursive tracking solution and Gaussian process (GP) regression with a specific class of spatio-temporal covariance. This result allows to use standard hyperparameter estimation techniques from the Gaussian process framework to determine the parameters of the KRLS-T algorithm. Most notably, it allows to estimate the optimal forgetting factor in a principled manner. We include results on different benchmark data sets that offer interesting new insights.
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