A General Linear Non-Gaussian State-Space Model: Identifiability, Identification, and Applications

Kun Zhang, Aapo Hyvärinen
Proceedings of the Asian Conference on Machine Learning, PMLR 20:113-128, 2011.

Abstract

State-space modeling provides a powerful tool for system identification and prediction. In linear state-space models the data are usually assumed to be Gaussian and the models have certain structural constraints such that they are identifiable. In this paper we propose a non-Gaussian state-space model which does not have such constraints. We prove that this model is fully identifiable. We then propose an efficient two-step method for parameter estimation: one first extracts the subspace of the latent processes based on the temporal information of the data, and then performs multichannel blind deconvolution, making use of both the temporal information and non-Gaussianity. We conduct a series of simulations to illustrate the performance of the proposed method. Finally, we apply the proposed model and parameter estimation method on real data, including major world stock indices and magnetoencephalography (MEG) recordings. Experimental results are encouraging and show the practical usefulness of the proposed model and method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v20-zhang11, title = {A General Linear Non-{G}aussian State-Space Model: Identifiability, Identification, and Applications}, author = {Zhang, Kun and Hyvärinen, Aapo}, booktitle = {Proceedings of the Asian Conference on Machine Learning}, pages = {113--128}, year = {2011}, editor = {Hsu, Chun-Nan and Lee, Wee Sun}, volume = {20}, series = {Proceedings of Machine Learning Research}, address = {South Garden Hotels and Resorts, Taoyuan, Taiwain}, month = {14--15 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v20/zhang11/zhang11.pdf}, url = {https://proceedings.mlr.press/v20/zhang11.html}, abstract = {State-space modeling provides a powerful tool for system identification and prediction. In linear state-space models the data are usually assumed to be Gaussian and the models have certain structural constraints such that they are identifiable. In this paper we propose a non-Gaussian state-space model which does not have such constraints. We prove that this model is fully identifiable. We then propose an efficient two-step method for parameter estimation: one first extracts the subspace of the latent processes based on the temporal information of the data, and then performs multichannel blind deconvolution, making use of both the temporal information and non-Gaussianity. We conduct a series of simulations to illustrate the performance of the proposed method. Finally, we apply the proposed model and parameter estimation method on real data, including major world stock indices and magnetoencephalography (MEG) recordings. Experimental results are encouraging and show the practical usefulness of the proposed model and method.} }
Endnote
%0 Conference Paper %T A General Linear Non-Gaussian State-Space Model: Identifiability, Identification, and Applications %A Kun Zhang %A Aapo Hyvärinen %B Proceedings of the Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2011 %E Chun-Nan Hsu %E Wee Sun Lee %F pmlr-v20-zhang11 %I PMLR %P 113--128 %U https://proceedings.mlr.press/v20/zhang11.html %V 20 %X State-space modeling provides a powerful tool for system identification and prediction. In linear state-space models the data are usually assumed to be Gaussian and the models have certain structural constraints such that they are identifiable. In this paper we propose a non-Gaussian state-space model which does not have such constraints. We prove that this model is fully identifiable. We then propose an efficient two-step method for parameter estimation: one first extracts the subspace of the latent processes based on the temporal information of the data, and then performs multichannel blind deconvolution, making use of both the temporal information and non-Gaussianity. We conduct a series of simulations to illustrate the performance of the proposed method. Finally, we apply the proposed model and parameter estimation method on real data, including major world stock indices and magnetoencephalography (MEG) recordings. Experimental results are encouraging and show the practical usefulness of the proposed model and method.
RIS
TY - CPAPER TI - A General Linear Non-Gaussian State-Space Model: Identifiability, Identification, and Applications AU - Kun Zhang AU - Aapo Hyvärinen BT - Proceedings of the Asian Conference on Machine Learning DA - 2011/11/17 ED - Chun-Nan Hsu ED - Wee Sun Lee ID - pmlr-v20-zhang11 PB - PMLR DP - Proceedings of Machine Learning Research VL - 20 SP - 113 EP - 128 L1 - http://proceedings.mlr.press/v20/zhang11/zhang11.pdf UR - https://proceedings.mlr.press/v20/zhang11.html AB - State-space modeling provides a powerful tool for system identification and prediction. In linear state-space models the data are usually assumed to be Gaussian and the models have certain structural constraints such that they are identifiable. In this paper we propose a non-Gaussian state-space model which does not have such constraints. We prove that this model is fully identifiable. We then propose an efficient two-step method for parameter estimation: one first extracts the subspace of the latent processes based on the temporal information of the data, and then performs multichannel blind deconvolution, making use of both the temporal information and non-Gaussianity. We conduct a series of simulations to illustrate the performance of the proposed method. Finally, we apply the proposed model and parameter estimation method on real data, including major world stock indices and magnetoencephalography (MEG) recordings. Experimental results are encouraging and show the practical usefulness of the proposed model and method. ER -
APA
Zhang, K. & Hyvärinen, A.. (2011). A General Linear Non-Gaussian State-Space Model: Identifiability, Identification, and Applications. Proceedings of the Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 20:113-128 Available from https://proceedings.mlr.press/v20/zhang11.html.

Related Material