Kernel Recursive Least-Squares Tracker for Time-Varying Regression

In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose, we first derive the standard KRLS equations from a Bayesian perspective (including a sensible approach to pruning) and then take advanta...

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Vydáno v:	IEEE transaction on neural networks and learning systems Ročník 23; číslo 8; s. 1313 - 1326
Hlavní autoři:	Van Vaerenbergh, S., Lazaro-Gredilla, M., Santamaria, I.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.08.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Adaptive filtering Adaptive filters Algorithm design and analysis Algorithms Applied sciences Bayesian inference Bayesian methods Computer science; control theory; systems Confidence intervals Data processing. List processing. Character string processing Exact sciences and technology Gaussian processes Kernel kernel methods kernel recursive least-squares (KRLS) Kernels Least squares method Least squares methods Mathematical analysis Mathematical models Memory organisation. Data processing Recursive Software Studies Tracking Bayes estimation Forgetting Tracking Adaptive algorithm kernel recursive least-squares (KRLS) Adaptive filtering Non stationary condition Recursive algorithm Modeling Confidence interval Kernel method Time varying system Gaussian process Efficiency Least squares method Gaussian processes kernel methods Pruning(tree) Bayesian inference
ISSN:	2162-237X, 2162-2388
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Popis
Shrnutí:	In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose, we first derive the standard KRLS equations from a Bayesian perspective (including a sensible approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in nonstationary scenarios. The resulting method is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner. In addition to its tracking ability, it has a number of appealing properties. It is online, requires a fixed amount of memory and computation per time step, incorporates regularization in a natural manner and provides confidence intervals along with each prediction. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	2162-237X 2162-2388
DOI:	10.1109/TNNLS.2012.2200500