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Multi-task Attributed Graphical Lasso

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Web and Big Data (APWeb-WAIM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12317))

Abstract

Sparse inverse covariance estimation, i.e., Graphical Lasso, can estimate the connections among a set of random variables basing on their observations. Recent research on Graphical Lasso has been extended to multi-task settings, where multiple graphs sharing the same set of variables are estimated collectively to reduce variances. However, different tasks usually involve different variables. For example, when we want to estimate gene networks w.r.t different diseases simultaneously, the related gene sets vary. In this paper, we study the problem of multi-task Graphical Lasso where the tasks may involve different variable sets. To share information across tasks, we consider the attributes of variables and assume that the structures of graphs are not only determined by observations, but influenced by attributes. We formulate the problem of learning multiple graphs jointly with observations and attributes, i.e., Multi-task Attributed Graphical Lasso (MAGL), and propose an effective algorithm to solve it. We rely on the LogDet divergence to explore latent relations between attributes of the variables and linkage structures among the variables. Multiple precision matrices and a projection matrix are optimized such that the \(\ell _1\)-penalized negative log-likelihood and the divergence are minimized.

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Acknowledgement

This work is supported in part by the Shanghai Science and Technology Development Fund No. 19511121204, No. 19DZ1200802, and the National Natural Science Foundation of China Projects No. U1636207, No. U1936213.

Author information

Authors and Affiliations

  1. School of Computer Science, Shanghai Key Laboratory of Data Science, Fudan University, Shanghai, China

    Yao Zhang, Yun Xiong & Yangyong Zhu

  2. Shanghai Institute for Advanced Communication and Data Science, Fudan University, Shanghai, China

    Yun Xiong & Yangyong Zhu

  3. Worcester Polytechnic Institute, Worcester, MA, USA

    Xiangnan Kong & Xinyue Liu

Authors
  1. Yao Zhang
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  2. Yun Xiong
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  3. Xiangnan Kong
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  4. Xinyue Liu
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  5. Yangyong Zhu
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Corresponding author

Correspondence to Yun Xiong .

Editor information

Editors and Affiliations

  1. Tianjin University, Tianjin, China

    Xin Wang

  2. University of Melbourne, Melbourn, NSW, Australia

    Rui Zhang

  3. Kyung Hee University, Yongin, Korea (Republic of)

    Young-Koo Lee

  4. Nanjing University of Information Science and Technology, Nanjing, China

    Le Sun

  5. Kangwon National University, Chunchon, Korea (Republic of)

    Yang-Sae Moon

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Zhang, Y., Xiong, Y., Kong, X., Liu, X., Zhu, Y. (2020). Multi-task Attributed Graphical Lasso. In: Wang, X., Zhang, R., Lee, YK., Sun, L., Moon, YS. (eds) Web and Big Data. APWeb-WAIM 2020. Lecture Notes in Computer Science(), vol 12317. Springer, Cham. https://doi.org/10.1007/978-3-030-60259-8_49

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  • DOI: https://doi.org/10.1007/978-3-030-60259-8_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-60258-1

  • Online ISBN: 978-3-030-60259-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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