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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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 23; no. 8; pp. 1313 - 1326
Main Authors: Van Vaerenbergh, S., Lazaro-Gredilla, M., Santamaria, I.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2012.2200500