Skip to main content
SpringerLink
Log in

Optimality of Multiple Decision Statistical Procedure for Gaussian Graphical Model Selection

  • Conference paper
  • First Online:
Learning and Intelligent Optimization (LION 12 2018)

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

Included in the following conference series:

  • 1509 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, 3rd edn. Wiley-Interscience, New York (2003)

    MATH  Google Scholar 

  2. Drton, M., Perlman, M.: Multiple testing and error control in Gaussian graphical model selection. Stat. Sci. 22(3), 430–449 (2007)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  4. Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996)

    MATH  Google Scholar 

  5. Lehmann, E.L.: A theory of some multiple decision problems, I. Ann. Math. Stat. 28, 1–25 (1957)

    Article  MathSciNet  Google Scholar 

  6. Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses. Springer, New York (2005)

    MATH  Google Scholar 

  7. Wald, A.: Statistical Decision Functions. Wiley, New York (1950)

    MATH  Google Scholar 

  8. Wainwright, M.J., Jordan, M.I.: Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1(1–2), 1–305 (2008)

    Article  Google Scholar 

Download references

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.

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander P. Koldanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Petr A. Koldanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05347-5

  • Online ISBN: 978-3-030-05348-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation