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Optimality of Multiple Decision Statistical Procedure for Gaussian Graphical Model Selection

  • Valery A. Kalyagin
  • Alexander P. Koldanov
  • Petr A. Koldanov
  • Panos M. Pardalos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11353)

Abstract

Gaussian graphical model selection is a statistical problem that identifies the Gaussian graphical model from observations. Existing Gaussian graphical model selection methods focus on the error rate for incorrect edge inclusion. However, when comparing statistical procedures, it is also important to take into account the error rate for incorrect edge exclusion. To handle this issue we consider the graphical model selection problem in the framework of multiple decision theory. We show that the statistical procedure based on simultaneous inference with UMPU individual tests is optimal in the class of unbiased procedures.

Keywords

Gaussian graphical models Multiple Decision Optimal multiple decision statistical procedures Unbiased multiple decision statistical procedures 

Notes

Acknowledgments

The Sects. 1 and 2 of the article were prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE). The Sect. 4 was prepared with a support of RSF grant 14-41-00039.

References

  1. 1.
    Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, 3rd edn. Wiley-Interscience, New York (2003)zbMATHGoogle Scholar
  2. 2.
    Drton, M., Perlman, M.: Multiple testing and error control in Gaussian graphical model selection. Stat. Sci. 22(3), 430–449 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Koldanov, P., Koldanov, A., Kalyagin, V., Pardalos, P.: Uniformly most powerful unbiased test for conditional independence in Gaussian graphical model. Stat. Probab. Lett. 122, 90–95 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996)zbMATHGoogle Scholar
  5. 5.
    Lehmann, E.L.: A theory of some multiple decision problems, I. Ann. Math. Stat. 28, 1–25 (1957)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses. Springer, New York (2005)zbMATHGoogle Scholar
  7. 7.
    Wald, A.: Statistical Decision Functions. Wiley, New York (1950)zbMATHGoogle Scholar
  8. 8.
    Wainwright, M.J., Jordan, M.I.: Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1(1–2), 1–305 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Valery A. Kalyagin
    • 1
    • 2
  • Alexander P. Koldanov
    • 1
    • 2
  • Petr A. Koldanov
    • 1
    • 2
  • Panos M. Pardalos
    • 1
    • 2
  1. 1.Laboratory of Algorithms and Technologies for Network AnalysisNational Research University Higher School of EconomicsNizhny NovgorodRussia
  2. 2.Center for Applied OptimizationUniversity of FloridaGainesvilleUSA

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