Skip to main content

Ensemble Learning in Non-Gaussian Data Assimilation

Part of the Lecture Notes in Computer Science book series (LNISA,volume 8964)

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-25138-7_21
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-25138-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   79.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Notes

  1. 1.

    MAP problem can also be solved.

  2. 2.

    Note that this problem is not the same as a Wiener filtering problem.

References

  1. Alspach, D.L., Sorenson, H.W.: Nonlinear bayesian estimation using Gaussian sum approximations. IEEE Trans. Autom. Control. 17, 439–448 (1972)

    CrossRef  MATH  Google Scholar 

  2. 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)

    CrossRef  Google Scholar 

  3. Bengtsson, T., Snyder, C., Nychka, D.: Toward a nonlinear ensemble filter for high-dimensional systems. J. Geophys. Res. 108, 8775 (2003)

    CrossRef  Google Scholar 

  4. Choi, S.C., Wette, R.: Maximum likelihood estimation of the parameters of the gamma distribution and their bias. Technometrics 11, 683–690 (1969)

    CrossRef  MATH  Google Scholar 

  5. Dovera, L., Rossa, E.D.: Multimodal ensemble kalman filtering using Gaussian mixture models. Comput. Geosci. 15, 307–323 (2011)

    CrossRef  MATH  Google Scholar 

  6. Dzeroski, S., Zenko, B.: Is combining classifiers better than selecting the best one? Mach. Learni. 54(3), 255–273 (2004). Morgan Kaufmann

    CrossRef  MATH  Google Scholar 

  7. Evensen, G.: The ensemble kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367 (2003)

    CrossRef  Google Scholar 

  8. Frei, M., Kunsch, H.R.: Mixture ensemble kalman filters. Comput. Stat. Data Anal. 58, 127–138 (2013)

    MathSciNet  CrossRef  MATH  Google Scholar 

  9. Gama, J., Brazdil, P.: Cascade generalization. Mach. Learn. 41(3), 315–343 (2000)

    CrossRef  MATH  Google Scholar 

  10. Gelb, A.: Applied Optimal Estimation. The MIT Press, Cambridge (1974)

    Google Scholar 

  11. 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)

    CrossRef  Google Scholar 

  12. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    CrossRef  Google Scholar 

  13. McLachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions. Wiley, Hoboken (2008)

    CrossRef  MATH  Google Scholar 

  14. Tagade, P.M., Ravela, S.: A quadratic information measure for data assimilation. In: American Control Conference 2014, Portland, USA (2014)

    Google Scholar 

  15. Ravela, S., Emanuel, K., McLaughlin, D.: Data assimilation by field alignment. Phys. D 230, 127–145 (2007)

    MathSciNet  CrossRef  MATH  Google Scholar 

  16. Ravela, S., McLaughlin, D.: Fast ensemble smoothing. Ocean Dyn. 57, 123–134 (2007)

    CrossRef  Google Scholar 

  17. Ravela, S.: Spatial inference for coherent geophysical fluids by appearance and geometry. In: Winter Conference on Applications of Computer Vision (2014)

    Google Scholar 

  18. Smith, K.W.: Cluster ensemble kalman filter. Tellus 59, 749–757 (2007)

    CrossRef  Google Scholar 

  19. 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)

    CrossRef  Google Scholar 

  20. 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

    Google Scholar 

  21. David, H.W.: Stacked generalization. Neural Netw. 5, 241–259 (1992)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Hansjörg Seybold or Sai Ravela .

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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)