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Optimality of Multiple Decision Statistical Procedure for Gaussian Graphical Model Selection

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Learning and Intelligent Optimization (LION 12 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11353))

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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.

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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.

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Authors and Affiliations

  1. Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, Bolshaya Pecherskaya 25/12, Nizhny Novgorod, Russia

    Valery A. Kalyagin, Alexander P. Koldanov, Petr A. Koldanov & Panos M. Pardalos

  2. Center for Applied Optimization, University of Florida, 401 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611-6595, USA

    Valery A. Kalyagin, Alexander P. Koldanov, Petr A. Koldanov & Panos M. Pardalos

Authors
  1. Valery A. Kalyagin
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  2. Alexander P. Koldanov
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  3. Petr A. Koldanov
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  4. Panos M. Pardalos
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Corresponding author

Correspondence to Valery A. Kalyagin .

Editor information

Editors and Affiliations

  1. University of Trento, Trento, Italy

    Roberto Battiti

  2. University of Trento, Trento, Italy

    Mauro Brunato

  3. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

  4. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Kalyagin, V.A., Koldanov, A.P., Koldanov, P.A., Pardalos, P.M. (2019). Optimality of Multiple Decision Statistical Procedure for Gaussian Graphical Model Selection. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 12 2018. Lecture Notes in Computer Science(), vol 11353. Springer, Cham. https://doi.org/10.1007/978-3-030-05348-2_26

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  • DOI: https://doi.org/10.1007/978-3-030-05348-2_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05347-5

  • Online ISBN: 978-3-030-05348-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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