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Unsupervised State-Space Modeling Using Reproducing Kernels


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Authors

Tobar, Felipe 
Djuric, Petar M 
Mandic, Danilo P 

Abstract

A novel framework for the design of state-space models (SSMs) is proposed whereby the state-transition function of the model is parametrised using reproducing kernels. The nature of SSMs requires learning a latent function that resides in the state space and for which input-output sample pairs are not available, thus prohibiting the use of gradient-based supervised kernel learning. To this end, we then propose to learn the mixing weights of the kernel estimate by sampling from their posterior density using Monte Carlo methods. We first introduce an offline version of the proposed algorithm, followed by an online version which performs inference on both the parameters and the hidden state through particle filtering. The accuracy of the estimation of the state-transition function is first validated on synthetic data. Next, we show that the proposed algorithm outperforms kernel adaptive filters in the prediction of real-world time series, while also providing probabilistic estimates, a key advantage over standard methods.

Description

This is the accepted manuscript. The final version is available at http://dx.doi.org/10.1109/TSP.2015.2448527.

Keywords

Support vector regression, system identification, nonlinear filtering, Monte Carlo methods, state-space models

Journal Title

IEEE Transactions on Signal Processing

Conference Name

Journal ISSN

1053-587X
1941-0476

Volume Title

63

Publisher

Institute of Electrical and Electronics Engineers (IEEE)
Sponsorship
Felipe Tobar acknowledges financial support from EPSRC grant number EP/L000776/1.