Automatic Emulation by Adaptive Relevance Vector Machines

  • Luca Martino
  • Jorge Vicent
  • Gustau Camps-Valls
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10269)


This paper introduces an automatic methodology to construct emulators for costly radiative transfer models (RTMs). The proposed method is sequential and adaptive, and it is based on the notion of the acquisition function by which instead of optimizing the unknown RTM underlying function we propose to achieve accurate approximations. The proposed methodology combines the interpolation capabilities of a modified Relevance Vector Machine (RVM) with the accurate design of an acquisition function that favors sampling in low density regions and flatness of the interpolation function. The proposed Relevance Vector Machine Automatic Emulator (RAE) is illustrated in toy examples and for the construction of an optimal look-up-table for atmospheric correction based on MODTRAN5.


Radiative transfer model Relevance Vector Machines Emulation Self-learning Look-up table Interpolation MODTRAN 


  1. 1.
    Berk, A., Anderson, G., Acharya, P., Bernstein, L., Muratov, L., Lee, J., Fox, M., Adler-Golden, S., Chetwynd, J., Hoke, M., Lockwood, R., Gardner, J., Cooley, T., Borel, C., Lewis, P., Shettle, E.: MODTRAN5: 2006 update. The International Society for Optical Engineering (2006)Google Scholar
  2. 2.
    Beygelzimer, A., Dasgupta, S., Langford, J.: Importance-weighted active learning. In: International Conference on Machine Learning (ICML), pp. 49–56 (2009)Google Scholar
  3. 3.
    Bishop, C.M.: Pattern recognition. Mach. Learn. 128, 1–58 (2006)Google Scholar
  4. 4.
    Busby, D.: Hierarchical adaptive experimental design for Gaussian process emulators. Reliab. Eng. Syst. Saf. 94, 1183–1193 (2009)CrossRefGoogle Scholar
  5. 5.
    Camps-Valls, G., Verrelst, J., Muñoz Marí, J., Laparra, V., Mateo-Jiménez, F., Gomez-Dans, J.: A survey on Gaussian processes for earth observation data analysis. IEEE Geosci. Remote Sens. Mag. 4(2), 58–78 (2016)CrossRefGoogle Scholar
  6. 6.
    Chaloner, K., Verdinelli, I.: Bayesian experimental design: a review. Stat. Sci. 10(3), 237–304 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cohn, D., Ghahramani, Z., Jordan, M.: Active learning with statistical models. J. Artif. Intell. Res. 4, 129–145 (1996)zbMATHGoogle Scholar
  8. 8.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, New York (1991)CrossRefzbMATHGoogle Scholar
  9. 9.
    Currin, C., Mitchell, T., Morris, M., Ylvisaker, D.: A Bayesian approach to the design and analysis of computer experiments, September 1988Google Scholar
  10. 10.
    Dasgupta, S.: Analysis of a greedy active learning strategy. In: Advances in Neural Information Processing Systems (NIPS) 16(3), pp. 337–344 (2004)Google Scholar
  11. 11.
    Guanter, L., Richter, R., Kaufmann, H.: On the application of the MODTRAN4 atmospheric radiative transfer code to optical remote sensing. Int. J. Remote Sens. 30(6), 1407–1424 (2009)CrossRefGoogle Scholar
  12. 12.
    Gutmann, M.U., Corander, J.: Bayesian optimization for likelihood-free inference of simulator-based statistical models. J. Mach. Learn. Res. 16, 4256–4302 (2015)Google Scholar
  13. 13.
    Kirkpatrick, S.K., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Luengo, D., Martino, L.: Almost rejectionless sampling from Nakagami-m distributions (m \(\ge \) 1). IET Electron. Letters 48(24), 1559–1561 (2012)CrossRefGoogle Scholar
  15. 15.
    Martino, L., Elvira, V., Luengo, D., Corander, J., Louzada, F.: Orthogonal parallel MCMC methods for sampling and optimization. Digit. Signal Proc. 58, 64–84 (2016)CrossRefGoogle Scholar
  16. 16.
    Marvasti, F.: Nonuniform Sampling: Theory and Practice. Kluwer Academic Publishers, New York (2001)Google Scholar
  17. 17.
    McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Mockus, J.: Bayesian Approach to Global Optimization. Kluwer Academic Publishers, Dordrecht (1989)CrossRefzbMATHGoogle Scholar
  19. 19.
    Oakley, J.E., O’Hagan, A.: Probabilistic sensitivity analysis of complex models: a Bayesian approach. J. Roy. Stat. Soc. 66B, 751–769 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    O’Brien, T.E., Funk, G.M.: A gentle introduction to optimal design for regression models. Am. Stat. 57(4), 265–267 (2003)MathSciNetCrossRefGoogle Scholar
  21. 21.
    O’Hagan, A.: Curve fitting and optimal design for predictions. J. Roy. Stat. Soc. 40B, 1–42 (1978)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press, Cambridge (2005)zbMATHGoogle Scholar
  23. 23.
    Read, J., Martino, L., Luengo, D.: Efficient Monte Carlo optimization for multi-label classifier chains. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 1–5 (2013)Google Scholar
  24. 24.
    Rivera, J., Verrelst, J., Gómez-Dans, J., Muñoz Marí, J., Moreno, J., Camps-Valls, G.: An emulator toolbox to approximate radiative transfer models with statistical learning. Remote Sens. 7(7), 9347–9370 (2015)CrossRefGoogle Scholar
  25. 25.
    Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4, 409–423 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    da Silva Ferreira, G., Gamerman, D.: Optimal design in geostatistics under preferential sampling. Bayesian Anal. 10(3), 711–735 (2015)Google Scholar
  27. 27.
    Snoek, J., Larochelle, H., Adams, R.P.: Practical Bayesian optimization of machine learning algorithms. Neural Information Processing Systems (NIPS), pp. 1–9 (2012). arXiv:1206.2944 (2012)
  28. 28.
    Verrelst, J., Dethier, S., Rivera, J., Muñoz-Marí, J., Camps-Valls, G., Moreno, J.: Active learning methods for efficient hybrid biophysical variable retrieval. IEEE Geosci. Remote Sens. Lett. 13(7), 1012–1016 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Luca Martino
    • 1
  • Jorge Vicent
    • 1
  • Gustau Camps-Valls
    • 1
  1. 1.Image Processing Laboratory (IPL)Universitat de ValènciaValenciaSpain

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