Abstract
The demand for tractable non-Gaussian Bayesian estimation has increased the popularity of kernel and mixture density representations. Here, using Gaussian Mixture Models (GMM), we posit that the reduction of total variance also remains an important objective in non-linear filtering, particularly in the presence of bias. We propose multi-objective estimation as an essential ingredient in data assimilation.
Using Ensemble Learning, two relatively weak estimators, namely the EnKF and Mixture Ensemble Filter (MEnF), are combined to produce a strong one. The Boosted-MEnF (B-MEnF) stacks MEnF and EnKF to mitigate bias and uses cascade generalization to reduce variance. In the Lorenz-63 model, it lowers mixture complexity without resampling and reduces posterior variance without increasing estimation error.
Our MEnF is a purely ensemble-based GMM filter with a reduced dimensionality burden and without ad-hoc ensemble-mixture member associations. It is expressed as a compact ensemble transform which enables efficient fixed-interval and fixed-lag smoothers (MEnS) as well as the B-MEnF/S.
Keywords
- Data assimilation
- Gaussian mixture models
- Ensemble learning
- Multi-objective assimilation
- Non-linear filtering and smoothing
- Non-Gaussian estimation
This is a preview of subscription content, access via your institution.
Buying options
Notes
- 1.
MAP problem can also be solved.
- 2.
Note that this problem is not the same as a Wiener filtering problem.
References
Alspach, D.L., Sorenson, H.W.: Nonlinear bayesian estimation using Gaussian sum approximations. IEEE Trans. Autom. Control. 17, 439–448 (1972)
Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian bayesian tracking. IEEE Trans. Signal Proc. 50(2), 174–188 (2002)
Bengtsson, T., Snyder, C., Nychka, D.: Toward a nonlinear ensemble filter for high-dimensional systems. J. Geophys. Res. 108, 8775 (2003)
Choi, S.C., Wette, R.: Maximum likelihood estimation of the parameters of the gamma distribution and their bias. Technometrics 11, 683–690 (1969)
Dovera, L., Rossa, E.D.: Multimodal ensemble kalman filtering using Gaussian mixture models. Comput. Geosci. 15, 307–323 (2011)
Dzeroski, S., Zenko, B.: Is combining classifiers better than selecting the best one? Mach. Learni. 54(3), 255–273 (2004). Morgan Kaufmann
Evensen, G.: The ensemble kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367 (2003)
Frei, M., Kunsch, H.R.: Mixture ensemble kalman filters. Comput. Stat. Data Anal. 58, 127–138 (2013)
Gama, J., Brazdil, P.: Cascade generalization. Mach. Learn. 41(3), 315–343 (2000)
Gelb, A.: Applied Optimal Estimation. The MIT Press, Cambridge (1974)
Hoteit, I., Pham, D.T., Triantafyllou, G., Korres, G.: A new approximate solution of the optimal nonlinear filter for data assimilation in meteorology and oceanography. Mon. Wea. Rev. 136, 317–334 (2008)
Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)
McLachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions. Wiley, Hoboken (2008)
Tagade, P.M., Ravela, S.: A quadratic information measure for data assimilation. In: American Control Conference 2014, Portland, USA (2014)
Ravela, S., Emanuel, K., McLaughlin, D.: Data assimilation by field alignment. Phys. D 230, 127–145 (2007)
Ravela, S., McLaughlin, D.: Fast ensemble smoothing. Ocean Dyn. 57, 123–134 (2007)
Ravela, S.: Spatial inference for coherent geophysical fluids by appearance and geometry. In: Winter Conference on Applications of Computer Vision (2014)
Smith, K.W.: Cluster ensemble kalman filter. Tellus 59, 749–757 (2007)
Sondergaard, T., Lermusiaux, P.F.J.: Data assimilation with Gaussian mixture models using dynamically orthogonal field equations. Part 1. Theory and scheme. Mon. Wea. Rev. 141, 1737–1760 (2013)
Tagade, P., Seybold, H., Ravela, S.: Mixture ensembles for data assimilation in dynamic data-driven environmental systems. In: Proceedings of the International Conference on Computational Science, ICCS 2014, Cairns, Queensland, Australia, pp. 1266–1276, 10–12 June 2014
David, H.W.: Stacked generalization. Neural Netw. 5, 241–259 (1992)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Seybold, H., Ravela, S., Tagade, P. (2015). Ensemble Learning in Non-Gaussian Data Assimilation. In: Ravela, S., Sandu, A. (eds) Dynamic Data-Driven Environmental Systems Science. DyDESS 2014. Lecture Notes in Computer Science(), vol 8964. Springer, Cham. https://doi.org/10.1007/978-3-319-25138-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-25138-7_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25137-0
Online ISBN: 978-3-319-25138-7
eBook Packages: Computer ScienceComputer Science (R0)