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Efficient state-space inference of periodic latent force models

Efficient state-space inference of periodic latent force models
Efficient state-space inference of periodic latent force models
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is the case in many real world problems where these latent forces exhibit periodic behaviour. Given this, we develop a new sparse representation of LFMs which considerably improves their computational efficiency, as well as broadening their applicability, in a principled way, to domains with periodic or near periodic latent forces. Our approach uses a linear basis model to approximate one generative model for each periodic force. We assume that the latent forces are generated from Gaussian process priors and develop a linear basis model which fully expresses these priors. We apply our approach to model the thermal dynamics of real homes and show that it is effective in predicting day-ahead temperatures within the homes. We also apply our approach within queueing theory in which quasi-periodic arrival rates are modelled as latent forces. We demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs. Further, we show that state estimates obtained using periodic latent force models can reduce the root mean squared error to 59% compared to estimates from non-periodic models and 84% compared to the nearest rival approach which is the Resonator model.
2337-2397
Reece, S.
c0ccfc80-2885-4b03-9428-b7dd73e8fa63
Roberts, S.
fc6a3991-f095-4a92-8501-56faabcfbd90
Ghosh, Siddhartha
abaf1e1d-3b5f-4a61-913e-e61273ed3790
Rogers, Alex
f9130bc6-da32-474e-9fab-6c6cb8077fdc
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Reece, S.
c0ccfc80-2885-4b03-9428-b7dd73e8fa63
Roberts, S.
fc6a3991-f095-4a92-8501-56faabcfbd90
Ghosh, Siddhartha
abaf1e1d-3b5f-4a61-913e-e61273ed3790
Rogers, Alex
f9130bc6-da32-474e-9fab-6c6cb8077fdc
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Reece, S., Roberts, S., Ghosh, Siddhartha, Rogers, Alex and Jennings, Nicholas R. (2014) Efficient state-space inference of periodic latent force models. Journal of Machine Learning Research, 15, 2337-2397.

Record type: Article

Abstract

Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is the case in many real world problems where these latent forces exhibit periodic behaviour. Given this, we develop a new sparse representation of LFMs which considerably improves their computational efficiency, as well as broadening their applicability, in a principled way, to domains with periodic or near periodic latent forces. Our approach uses a linear basis model to approximate one generative model for each periodic force. We assume that the latent forces are generated from Gaussian process priors and develop a linear basis model which fully expresses these priors. We apply our approach to model the thermal dynamics of real homes and show that it is effective in predicting day-ahead temperatures within the homes. We also apply our approach within queueing theory in which quasi-periodic arrival rates are modelled as latent forces. We demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs. Further, we show that state estimates obtained using periodic latent force models can reduce the root mean squared error to 59% compared to estimates from non-periodic models and 84% compared to the nearest rival approach which is the Resonator model.

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Published date: July 2014
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 363372
URI: https://eprints.soton.ac.uk/id/eprint/363372
PURE UUID: 5cc871f0-2fb8-4154-b3b1-5cf026a0a26b

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Date deposited: 23 Mar 2014 09:25
Last modified: 19 Jul 2019 21:15

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