Optimality of Multiple Decision Statistical Procedure for Gaussian Graphical Model Selection

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


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.


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



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.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Valery A. Kalyagin
    • 1
    • 2
    Email author
  • 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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