Bayesian Gaussian process models for multi-sensor time series prediction

doi:10.1017/CBO9780511984679.017

16 - Bayesian Gaussian process models for multi-sensor time series prediction

from V - Nonparametric models

Published online by Cambridge University Press: 07 September 2011

Michael A. Osborne ,

Alex Rogers ,

Stephen J. Roberts ,

Sarvapali D. Ramchurn and

Edited by

A. Taylan Cemgil and

Michael A. Osborne: Affiliation:
University of Oxford
Alex Rogers: Affiliation:
University of Southampton
Stephen J. Roberts: Affiliation:
University of Oxford
Sarvapali D. Ramchurn: Affiliation:
University of Southampton
Nick R. Jennings: Affiliation:
University of Southampton
David Barber: Affiliation:
University College London
A. Taylan Cemgil: Affiliation:
Boğaziçi Üniversitesi, Istanbul
Silvia Chiappa: Affiliation:
University of Cambridge

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Summary

Introduction

Sensor networks have recently generated a great deal of research interest within the computer and physical sciences, and their use for the scientific monitoring of remote and hostile environments is increasingly commonplace. While early sensor networks were a simple evolution of existing automated data loggers, that collected data for later offline scientific analysis, more recent sensor networks typically make current data available through the Internet, and thus, are increasingly being used for the real-time monitoring of environmental events such as floods or storm events (see [10] for a review of such environmental sensor networks).

Using real-time sensor data in this manner presents many novel challenges. However, more significantly for us, many of the information processing tasks that would previously have been performed offline by the owner or single user of an environmental sensor network (such as detecting faulty sensors, fusing noisy measurements from several sensors, and deciding how frequently readings should be taken), must now be performed in real-time on the mobile computers and PDAs carried by the multiple different users of the system (who may have different goals and may be using sensor readings for very different tasks). Importantly, it may also be necessary to use the trends and correlations observed in previous data to predict the value of environmental parameters into the future, or to predict the reading of a sensor that is temporarily unavailable (e.g. due to network outages).

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Type: Chapter
Information: Bayesian Time Series Models , pp. 341 - 362

DOI: https://doi.org/10.1017/CBO9780511984679.017 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2011

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References

[1] P., Abrahamsen. A review of Gaussian random fields and correlation functions. Technical Report 917, Norwegian Computing Center, Box 114, Blindern, N-0314 Oslo, Norway, 1997. 2nd edition.

[2] P., Boyle and M., Frean. Dependent Gaussian processes. In Advances in Neural Information Processing Systems 17, pages 217–224. The MIT Press, 2005.Google Scholar

[3] W., Chu and Z., Ghahramani. Gaussian processes for ordinal regression. Journal of Machine Learning Research, 6(1):1019, 2006.Google Scholar

[4] N. A. C., Cressie. Statistics for Spatial Data. John Wiley & Sons, 1991.Google Scholar

[5] A., Deshpande, C., Guestrin, S., Madden, J., Hellerstein and W., Hong. Model-driven data acquisition in sensor networks. In Proceedings of the Thirtieth International Conference on Very Large Data Bases (VLDB 2004), pages 588–599, 2004.Google Scholar

[6] E., Ertin. Gaussian process models for censored sensor readings. In Statistical Signal Processing, 2007. SSP'07. IEEE/SP 14th Workshop on, pages 665–669, 2007.Google Scholar

[7] M., Fuentes, A., Chaudhuri and D. H., Holland. Bayesian entropy for spatial sampling design of environmental data. Environmental and Ecological Statistics, 14:323–340, 2007.Google Scholar

[8] A., Genz. Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1(2):141–149, 1992.Google Scholar

[9] A., Girard, C., Rasmussen, J., Candela and R., Murray-Smith. Gaussian process priors with uncertain inputs – application to multiple-step ahead time series forecasting. In Advances in Neural Information Processing Systems 16. MIT Press, 2003.Google Scholar

[10] J. K., Hart and K., Martinez. Environmental Sensor Networks: A revolution in the earth system science?Earth-Science Reviews, 78:177–191, 2006.Google Scholar

[11] A. H., Jazwinski. Stochastic Processes and Filtering Theory. Academic Press, 1970.Google Scholar

[12] A., Kapoor and E., Horvitz. On discarding, caching, and recalling samples in active learning. In Uncertainty in Artificial Intelligence, 2007.Google Scholar

[13] A., Krause, C., Guestrin, A., Gupta and J., Kleinberg. Near-optimal sensor placements: maximizing information while minimizing communication cost. In Proceedings of the Fifth International Conference on Information Processing in Sensor Networks (IPSN '06), pages 2–10, Nashville, Tennessee, USA, 2006.Google Scholar

[14] S. M., Lee and S. J., Roberts. Multivariate time series forecasting in incomplete environments. Technical Report PARG-08-03. Available at www.robots.ox.ac.uk/∼parg/publications.html. University of Oxford, December 2008.

[15] D. J. C., MacKay. Information-based objective functions for active data selection. Neural Computation, 4(4):590–604, 1992.Google Scholar

[16] D. J. C., MacKay. Information Theory, Inference and Learning Algorithms. Cambridge University Press, 2002.Google Scholar

[17] A., O'Hagan. Monte Carlo is fundamentally unsound. The Statistician, 36:247–249, 1987.Google Scholar

[18] A., O'Hagan. Bayes-Hermite quadrature. Journal of Statistical Planning and Inference, 29:245–260, 1991.Google Scholar

[19] M., Osborne and S. J., Roberts. Gaussian processes for prediction. Technical Report PARG-07-01. Available at www.robots.ox.ac.uk/∼parg/publications.html, University of Oxford, September 2007.

[20] J., Pinheiro and D., Bates. Unconstrained parameterizations for variance-covariance matrices. Statistics and Computing, 6:289–296, 1996.Google Scholar

[21] C. E., Rasmussen and Z., Ghahramani. Bayesian Monte Carlo. In Advances in Neural Information Processing Systems 15, pages 489–496. The MIT Press, 2003.Google Scholar

[22] C. E., Rasmussen and C. K. I., Williams. Gaussian Processes for Machine Learning. MIT Press, 2006.Google Scholar

[23] M. J., Sasena. Flexibility and effciency enhancements for constrained global design optimization with Kriging approximations. PhD thesis, University of Michigan, 2002.

[24] S., Seo, M., Wallat, T., Graepel and K., Obermayer. Gaussian process regression: active data selection and test point rejection. In Neural Networks, 2000. IJCNN 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on, volume 3, 2000.Google Scholar

[25] M. L., Stein. Space-time covariance functions. Journal of the American Statistical Association, 100(469):310–322, 2005.Google Scholar

[26] Y. W., Teh, M., Seeger and M. I., Jordan. Semiparametric latent factor models. In Proceedings of the Conference on Artificial Intelligence and Statistics, pages 333–340, 2005.Google Scholar

[27] The Math Works. MATLAB R2007a, 2007.

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