Abstract
We study a data assimilation problem using Gaussian processes (GPs) where the GPs act as latent variables for the observations. Inference is done using a convenient parameterisation and sequential learning for a faster algorithm. We are addressing the disadvantage of the GPs, namely the quadratic scaling of the parameters with data and eliminate the scaling by using a fixed number of parameters. The result is a sparse representation that allows us to treat problems with a large number of observations. We apply our method to the prediction of wind fields over the ocean surface from scatterometer data.
This article is a revised version of “Online Learning of Wind-Field Models”, published in the Proceedings of the International Conference on Artificial Neural Networks, Vienna, 2001.
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References
Bernardo, J. M. and Smith, A. F. (1994). Bayesian Theory. John Wiley & Sons.
Bishop, C. M. (1995). Neural Networks for Pattern Recognition. Oxford University Press, New York, N.Y.
Csato, L., Cornford, D., and Opper, M. (2001). Online learning of wind-field models. In International Conference on Artificial Neural Networks, pages 300–307.
Csato, L. and Opper, M. (2002). Sparse on-line Gaussian Processes. Neural Computation, 14(3):641–669.
Csato, L. and Opper, M. (prep). Greedy sparse approximation to Gaussian Processes by relative entropy projection. Technical report, Neural Computing Research Group.
Daley, R. (1991). Atmospheric Data Analysis. Cambridge University Press, Cambridge.
Evans, D. J., Cornford, D., and Nabney, I. T. (2000). Structured neural network modelling of multi-valued functions for wind retrieval from scatterometer measurements. Neurocomputing Letters, 30:23–30.
Evensen, G. (2001). Sequential data assimilation for nonlinear dynamics: the ensemble Kalmam Filter. In Pinardi, N. and Woods, J. D., editors, Ocean Forecasting: Conceptual basis and applications. Springer-Verlag.
Ide, K., Courtier, P., Ghil, M., and Lorenc, A. C. (1997). Unified notation for data assimilation: Operational, sequential and variational. Journal of the Meteorological Society of Japan, 75:181–189.
Kimeldorf, G. and Wahba, G. (1971). Some results on Tchebycheffian spline functions. J. Math. Anal. Applic., 33:82–95.
Lorenc, A. C. (1986). Analysis methods for numerical weather prediction. Quarterly Journal of the Royal Meteorological Society, 112:1177–1194.
Minka, T. P. (2000). Expectation Propagation for Approximate Bayesian Inference. PhD thesis, Dep. of Electrical Eng. and Comp. Sci.; MIT.
Nabney, I. T., Cornford, D., and Williams, C. K. I. (2000). Bayesian inference for wind field retrieval. Neurocomputing Letters, 30:3–11.
Offiler, D. (1994). The calibration of ERS-1 satellite scatterometer winds. Journal of Atmospheric and Oceanic Technology, 11:1002–1017.
Opper, M. (1998). A Bayesian approach to online learning. In On-Line Learning in Neural Networks, pages 363–378. Cambridge Univ. Press.
Opper, M. and Winther, O. (1999). Gaussian processes and SVM: Mean field results and leave-one-out estimator. In Smola, A., Bartlett, P., Schoelkopf, B., and Schuurmans, C., editors, Advances in Large Margin Classifiers, pages 43–65. The MIT Press, Cambridge, MA.
Roweis, S. and Ghahramani, Z. (2001). An EM algorithm for identification of nonlinear dynamical systems. In Haykin, S., editor, Kalman Filtering and Neural Networks. Wiley.
Schoelkopf, B., Burges, C. J., and Smola, A. J., editors (1999). Advances in kernel methods (Support Vector Learning). The MIT Press.
Stoffelen, A. and Anderson, D. (1997). Ambiguity removal and assimiliation of scatterometer data. Quarterly Journal of the Royal Meteorological Society, 123:491–518.
Tipping, M. (2000). The Relevance Vector Machine. In Solla, S. A., Leen, T. K., and Mueller, K.-R., editors, NIPS, volume 12, pages 652–658. The MIT Press.
Vapnik, V. N. (1995). The Nature of Statistical Learning Theory. Springer-Verlag, New York, NY.
Williams, C. K. I. and Rasmussen, C. E. (1996). Gaussian processes for regression. In Touretzky, D. S., Mozer, M. C., and Hasselmo, M. E., editors, NIPS, volume 8. The MIT Press.
Wolf, D. R. (1999). A Bayesian reflection on surfaces. Entropy, l(4):69–98.
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Csato, L., Cornford, D., Opper, M. (2002). Data Assimilation with Sequential Gaussian Processes. In: Winkler, J., Niranjan, M. (eds) Uncertainty in Geometric Computations. The Springer International Series in Engineering and Computer Science, vol 704. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0813-7_3
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DOI: https://doi.org/10.1007/978-1-4615-0813-7_3
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