The kernel Kalman rule: efficient nonparametric inference with recursive least squares

Gebhardt, G. H. W. and Kupcsik, A. and Neumann, G. (2017) The kernel Kalman rule: efficient nonparametric inference with recursive least squares. In: Thirty-First AAAI Conference on Artificial Intelligence, 4 - 9 February 2017, San Francisco, California, USA.

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Abstract

Nonparametric inference techniques provide promising tools
for probabilistic reasoning in high-dimensional nonlinear systems.
Most of these techniques embed distributions into reproducing
kernel Hilbert spaces (RKHS) and rely on the kernel
Bayes’ rule (KBR) to manipulate the embeddings. However,
the computational demands of the KBR scale poorly
with the number of samples and the KBR often suffers from
numerical instabilities. In this paper, we present the kernel
Kalman rule (KKR) as an alternative to the KBR. The derivation
of the KKR is based on recursive least squares, inspired
by the derivation of the Kalman innovation update. We apply
the KKR to filtering tasks where we use RKHS embeddings
to represent the belief state, resulting in the kernel Kalman filter
(KKF). We show on a nonlinear state estimation task with
high dimensional observations that our approach provides a
significantly improved estimation accuracy while the computational
demands are significantly decreased.

Keywords:Filtering, Kernel-Based Methods
Subjects:G Mathematical and Computer Sciences > G760 Machine Learning
Divisions:College of Science > School of Computer Science
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ID Code:26739
Deposited On:17 Mar 2017 14:22

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