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Edge selection based on the geometry of dually flat spaces for Gaussian graphical models

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Abstract

We propose a method for selecting edges in undirected Gaussian graphical models. Our algorithm takes after our previous work, an extension of Least Angle Regression (LARS), and it is based on the information geometry of dually flat spaces. Non-diagonal elements of the inverse of the covariance matrix, the concentration matrix, play an important role in edge selection. Our iterative method estimates these elements and selects covariance models simultaneously. A sequence of pairs of estimates of the concentration matrix and an independence graph is generated, whose length is the same as the number of non-diagonal elements of the matrix. In our algorithm, the next estimate of the graph is the nearest graph to the latest estimate of the concentration matrix. The next estimate of the concentration matrix is not just the projection of the latest estimate, and it is shrunk to the origin. We describe the algorithm and show results for some datasets. Furthermore, we give some remarks on model identification and prediction.

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Acknowledgements

This research was supported in part by Grant-in-Aid for Scientific Research (23300104, 23650144), by Global COE Program “The research and training center for new development in mathematics,” MEXT, Japan, and by the Aihara Project, the FIRST program from JSPS, initiated by CSTP.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Yoshihiro Hirose & Fumiyasu Komaki

  2. RIKEN Brain Science Institute, 2-1, Hirosawa, Wako City, Saitama, 351-0198, Japan

    Fumiyasu Komaki

Authors
  1. Yoshihiro Hirose
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  2. Fumiyasu Komaki
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Correspondence to Yoshihiro Hirose.

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Hirose, Y., Komaki, F. Edge selection based on the geometry of dually flat spaces for Gaussian graphical models. Stat Comput 23, 793–800 (2013). https://doi.org/10.1007/s11222-012-9347-3

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  • DOI: https://doi.org/10.1007/s11222-012-9347-3

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