Maximum Likelihood Estimation Based on Random Subspace EDA: Application to Extrasolar Planet Detection

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10593)

Abstract

This paper addresses maximum likelihood (ML) estimation based model fitting in the context of extrasolar planet detection. This problem is featured by the following properties: (1) the candidate models under consideration are highly nonlinear; (2) the likelihood surface has a huge number of peaks; (3) the parameter space ranges in size from a few to dozens of dimensions. These properties make the ML search a very challenging problem, as it lacks any analytical or gradient based searching solution to explore the parameter space. A population based searching method, called estimation of distribution algorithm (EDA), is adopted to explore the model parameter space starting from a batch of random locations. EDA is featured by its ability to reveal and utilize problem structures. This property is desirable for characterizing the detections. However, it is well recognized that EDAs can not scale well to large scale problems, as it consists of iterative random sampling and model fitting procedures, which results in the well-known dilemma curse of dimensionality. A novel mechanism to perform EDAs in interactive random subspaces spanned by correlated variables is proposed and the hope is to alleviate the curse of dimensionality for EDAs by performing the operations of sampling and model fitting in lower dimensional subspaces. The effectiveness of the proposed algorithm is verified via both benchmark numerical studies and real data analysis.

Keywords

Estimation of distribution Extrasolar planet detection Maximum likelihood estimation Nonlinear model Optimization Random subspace 

Notes

Acknowledgement

This work was partly supported by the National Natural Science Foundation (NSF) of China under grant No. 61571238, China Postdoctoral Science Foundation under grant Nos. 2015M580455 and 2016T90483, the Six Talents Peak Foundation of Jiangsu Province under grant No. XYDXXJS-CXTD-006 and the Scientific and Technological Support Project (Society) of Jiangsu Province under grant No. BE2016776.

References

  1. 1.
    Lissauer, J.J., Dawson, R.I., Tremaine, S.: Advances in exoplanet science from Kepler. Nature 513(7518), 336–344 (2014)CrossRefGoogle Scholar
  2. 2.
    Borucki, W.J., Koch, D., Basri, G., Batalha, N., Brown, T., Caldwell, D., Caldwell, J., Christensen-Dalsgaard, J., Cochran, W.D., DeVore, E., et al.: Kepler planet-detection mission: introduction and first results. Science 327(5968), 977–980 (2010)CrossRefGoogle Scholar
  3. 3.
    Loredo, T.J., Berger, J.O., Chernoff, D.F., Clyde, M.A., Liu, B.: Bayesian methods for analysis and adaptive scheduling of exoplanet observations. Stat. Methodol. 9(1), 101–114 (2012)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Wolszczan, A., Frail, D.A.: A planetary system around the millisecond pulsar PSR 1257+ 12. Nature 355(6356), 145–147 (1992)CrossRefGoogle Scholar
  5. 5.
    Desort, M., Lagrange, A.-M., Galland, F., Udry, S., Mayor, M.: Search for exoplanets with the radial-velocity technique: quantitative diagnostics of stellar activity. Astron. Astrophys. 473(3), 983–993 (2007)CrossRefGoogle Scholar
  6. 6.
    Liu, B.: Adaptive annealed importance sampling for multimodal posterior exploration and model selection with application to extrasolar planet detection. Astrophys. J. Suppl. Ser. 213(14), 1–16 (2014)Google Scholar
  7. 7.
    Baluev, R.V.: PlanetPack: a radial-velocity time-series analysis tool facilitating exoplanets detection, characterization, and dynamical simulations. Astron. Comput. 2, 18–26 (2013)CrossRefGoogle Scholar
  8. 8.
    Brewer, B.J., Donovan, C.P.: Fast Bayesian inference for exoplanet discovery in radial velocity data. Mon. Not. R. Astron. Soc. 448(4), 3206–3214 (2015)CrossRefGoogle Scholar
  9. 9.
    Zhang, Q., Muhlenbein, H.: On the convergence of a class of estimation of distribution algorithms. IEEE Trans. Evol. Comput. 8(2), 127–136 (2004)CrossRefGoogle Scholar
  10. 10.
    Pelikan, M., Goldberg, D.E., Lobo, F.G.: A survey of optimization by building and using probabilistic models. Comput. Optim. Appl. 21(1), 5–20 (2002)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Hauschild, M., Pelikan, M.: An introduction and survey of estimation of distribution algorithms. Swarm Evol. Comput. 1(3), 111–128 (2011)CrossRefGoogle Scholar
  12. 12.
    Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Liang, J., Qu, B., Suganthan, P., Hernández-Díaz, A.G.: Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Technical report, Computational Intelligence Lab, Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore (2013)Google Scholar
  14. 14.
    Trelea, I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85(6), 317–325 (2003)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Ros, R., Hansen, N.: A simple modification in CMA-ES achieving linear time and space complexity. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 296–305. Springer, Heidelberg (2008). doi:10.1007/978-3-540-87700-4_30 CrossRefGoogle Scholar
  16. 16.
    Larranaga, P., Lozano, J.A.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Dordrecht (2002)CrossRefMATHGoogle Scholar
  17. 17.
    Hansen, N.: CMA-ES source code. https://www.lri.fr/~hansen/cmaes_inmatlab.html
  18. 18.
    Tinney, C.G., Butler, R.P., Marcy, G.W., Jones, H.R., Laughlin, G., Carter, B.D., Bailey, J.A., O’Toole, S.: The 2:1 resonant exoplanetary system orbiting HD73526. Astrophys. J. 647(1), 594–599 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Computer ScienceNanjing University of Posts and TelecommunicationsNanjingChina
  2. 2.Jiangsu Key Laboratory of Big Data Security and Intelligent ProcessingNanjingChina

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