Skip to main content
SpringerLink
Log in

Multi-task attributed graphical lasso and its application in fund classification

  • Published:
World Wide Web Aims and scope Submit manuscript

Abstract

Sparse inverse covariance estimation, i.e., Graphical Lasso, reveals the underlying structure of graph for a set of variables on the basis of their observations. The estimated graphs can then facilitate a series of downstream tasks with graph mining techniques. Multi-task Graphical Lasso is designed for collectively estimating graphs sharing an identical set of variables, but it fails to contend with the situation when the tasks include different variables. In order to address this limitation, we propose Multi-task Attributed Graphical Lasso (MAGL) to learn graphs with observations and attributes jointly. Specifically, we introduce two concrete implementations, i.e., MAGL-LogDet and MAGL-HSIC, where the LogDet divergence and the Hilbert-Schmidt independence criterion are utilized respectively to explore latent relations between attributes of the variables and linkage structures among the variables. Experimental results show the effectiveness of MAGL-LogDet and MAGL-HSIC. We then apply MAGL to fund data and estimate stock graphs for each fund. We classify funds by using graph neural networks on the estimated graphs, and prove that we can benefit from MAGL in downstream tasks.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. We suppress superscript k for simplicity.

References

  1. Huang, S., Li, J., Sun, L., Ye, J., Fleisher, A., Wu, T., Chen, K., Reiman, E.: Alzheimer’s Disease NeuroImaging Initiative, others. Learning brain connectivity of alzheimer’s disease by sparse inverse covariance estimation. Neuroimage 50(3), 935–949 (2010)

    Article  Google Scholar 

  2. Fan, J., Liao, Y., Liu, H: An overview of the estimation of large covariance and precision matrices. Economet J 19(1) (2016)

  3. Giudici, P., Spelta, A.: Graphical network models for international financial flows. J. Bus. Econ. Stat. 34(1), 128–138 (2016)

    Article  MathSciNet  Google Scholar 

  4. Zhang, Y., Xiong, Y., Liu, X., Kong, X., Zhu, Y.: Meta-path graphical lasso for learning heterogeneous connectivities. In: SDM, pp. 642–650 (2017)

  5. Yin, H., Liu, X., Kong, X.: Coherent graphical lasso for brain network discovery. In: ICDM (2018)

  6. Mantegna, R.N.: Hierarchical structure in financial markets. Eur. Phys. J. B-Cond. Matter Complex Syst. 11(1), 193–197 (1999)

    Article  Google Scholar 

  7. Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441 (2008)

    Article  Google Scholar 

  8. Lee, W., Liu, Y.: Joint estimation of multiple precision matrices with common structures. JMLR 16(1), 1035–1062 (2015)

    MathSciNet  MATH  Google Scholar 

  9. Hara, S., Washio, T.: Common substructure learning of multiple graphical gaussian models. In: ECMLPKDD, pp. 1–16 (2011)

  10. Danaher, P., Wang, P., Witten, D. M.: The joint graphical lasso for inverse covariance estimation across multiple classes. J. R. Stat. Soc Ser. B Stat. Methodol. 76(2), 373–397 (2014)

    Article  MathSciNet  Google Scholar 

  11. Yang, S., Lu, Z., Shen, X., Wonka, P., Ye, J.: Fused multiple graphical lasso. SIOPT 25(2), 916–943 (2015)

    Article  MathSciNet  Google Scholar 

  12. Tao, Q., Huang, X., Wang, S., Xi, X., Li, L.: Multiple Gaussian graphical estimation with jointly sparse penalty. Signal Process. 128, 88–97 (2016)

    Article  Google Scholar 

  13. Kulis, B., Sustik, M., Dhillon, I.: Learning low-rank kernel matrices. In: ICML, pp. 505–512 (2006)

  14. Gretton, A., Bousquet, O., Smola, A., Schölkopf, B.: Measuring statistical dependence with Hilbert-Schmidt norms. In: Int. Conf. Algorithmic Learning Theory, vol. 16, pp. 63–78. Springer (2005)

  15. Kipf, T. N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv:1609.02907 (2016)

  16. Hsieh, C., Sustik, M. A., Dhillon, I. S., Ravikumar, P.D.: QUIC: Quadratic approximation for sparse inverse covariance estimation. JMLR 15(1), 2911–2947 (2014)

    MathSciNet  MATH  Google Scholar 

  17. Yuan, X.: Alternating direction methods for sparse covariance selection. Optimization Online (2009)

  18. Mazumder, R., Hastie, T.: The graphical lasso: New insights and alternatives. EJS 6, 2125 (2012)

    MathSciNet  MATH  Google Scholar 

  19. Cai, T., Liu, W., Luo, X.: A constrained l1 minimization approach to sparse precision matrix estimation. JASA 106(494), 594–607 (2011)

    Article  Google Scholar 

  20. Witten, D. M., Friedman, J. H., Simon, N.: New insights and faster computations for the graphical lasso. J. Comput. Graph. Stat. 20(4), 892–900 (2011)

    Article  MathSciNet  Google Scholar 

  21. Grechkin, M., Fazel, M., Witten, D., Lee, S.: Pathway graphical lasso. In: AAAI, pp. 2617–2623 (2015)

  22. Guo, J., Levina, E., Michailidis, G., Zhu, J.: Joint estimation of multiple graphical models. Biometrika 98(1), 1–15 (2011)

    Article  MathSciNet  Google Scholar 

  23. Yu, K, Guo, X., Liu, L., Li, J., Wang, H., Ling, Z., Wu, X: Causality-based feature selection: Methods and evaluations. ACM Computing Surveys (CSUR) 53(5), 1–36 (2020)

    Article  Google Scholar 

  24. Christina, H.-D., Nicolai, M., Jonas, P.: Invariant causal prediction for nonlinear models. J. Causal Inference 6(2) (2018)

  25. Zhu, S., Ng, I, Chen, Z: Causal discovery with reinforcement learning. arXiv:1906.04477 (2019)

  26. Wu, Z, Pan, S, Long, G, Jiang, J, Chang, X, Zhang, C.: Connecting the dots Multivariate time series forecasting with graph neural networks. In: Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 753–763 (2020)

  27. Ying, R., You, J., Morris, C., Ren, X.: William l hamilton, and jure leskovec: Hierarchical graph representation learning with differentiable pooling. arXiv:1806.08804 (2018)

  28. Cao, D., Wang, Y., Duan, J., Zhang, C., Zhu, X., Huang, C., Tong, Y., Xu, B., Bai, J., Tong, J., et al.: Spectral temporal graph neural network for multivariate time-series forecasting. Adv. Neural Inf. Process. Syst, 33 (2020)

  29. Bai, L., Yao, L., Li, C., Wang, X., Wang, C.: Adaptive graph convolutional recurrent network for traffic forecasting. arXiv:2007.02842 (2020)

  30. Davis, J. V., Dhillon, I. S.: Differential entropic clustering of multivariate gaussians. In: NeurIPS, pp. 337–344 (2007)

  31. Barshan, E., Ghodsi, A., Azimifar, Z., Jahromi, M. Z.: Supervised principal component analysis: visualization, classification and regression on subspaces and submanifolds. Pattern Recogn. 44(7), 1357–1371 (2011)

    Article  Google Scholar 

  32. Zhang, Y., Xiong, Y., Kong, X., Liu, X., Zhu, Y.: Multi-task attributed graphical lasso. In: APWeb-WAIM, pp. 670–684 (2020)

  33. Cristianini, N., Shawe-Taylor, J.: An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press (2000)

  34. Kang, Z., Peng, C., Cheng, J., Cheng, Q.: Logdet rank minimization with application to subspace clustering. Comput Intel Neurosc 2015, 68 (2015)

    Article  Google Scholar 

  35. Lutkepohl, H.: Handbook of matrices. Comput. Stat. Data Anal. 2 (25), 243 (1997)

    Google Scholar 

  36. Sun, Y., Han, J., Gao, J., itopicmodel, Y. Y. u.: Information network-integrated topic modeling. In: ICDM, pp. 493–502 (2009)

  37. Gentles, A. J., Plevritis, S. K., Majeti, R., Alizadeh, A. A.: Association of a leukemic stem cell gene expression signature with clinical outcomes in acute myeloid leukemia. JAMA 304(24), 2706–2715 (2010)

    Article  Google Scholar 

  38. Haferlach, T., Kohlmann, A., Wieczorek, L., Basso, G., Te Kronnie, G., Béné, M., De, VJ., Hernández, J. M., Hofmann, W., Mills, K. I., et al.: Clinical utility of microarray-based gene expression profiling in the diagnosis and subclassification of leukemia: report from the international microarray innovations in leukemia study group. Int. J. Clin. Oncol. 28(15), 2529–2537 (2010)

    Article  Google Scholar 

  39. Maaten, L. V. D., Hinton, G.: Visualizing data using t-sne. JMLR 9, 2579–2605 (2008)

    MATH  Google Scholar 

  40. Xu, K., Li, C., Tian, Y., Sonobe, T., Kawarabayashi, K.-I., Jegelka, S.: Representation learning on graphs with jumping knowledge networks. In: International Conference on Machine Learning, pp. 5453–5462. PMLR (2018)

  41. Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735–1780 (1997)

    Article  Google Scholar 

  42. Li, Z, Wang, X, Li, J, Zhang, Q: Deep attributed network representation learning of complex coupling and interaction. Knowl-Based Syst 212, 106618 (2021)

    Article  Google Scholar 

Download references

Funding

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

Author information

Authors and Affiliations

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

    Yao Zhang, Sijia Peng, Yun Xiong & Yangyong Zhu

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

    Yun Xiong & Yangyong Zhu

  3. Worcester Polytechnic Institute, Worcester, MA, USA

    Xiangnan Kong & Xinyue Liu

Authors
  1. Yao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sijia Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yun Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiangnan Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xinyue Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yangyong Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yun Xiong.

Ethics declarations

Conflicts of Interest/Competing interests

Not applicable.

Additional information

Availability of Data and Material

The data used in the paper is available at https://github.com/lunaaa95/lunahoho/tree/linux/data/Dataset.

Code availability

The codes are available at https://github.com/lunaaa95/lunahoho/tree/linux.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Yao Zhang and Sijia Peng contribute equally to this work.

This article belongs to the Topical Collection: Special Issue on Graph Data Management, Mining, and Applications Guest Editors: Xin Wang, Rui Zhang, and Young-Koo Lee

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Y., Peng, S., Xiong, Y. et al. Multi-task attributed graphical lasso and its application in fund classification. World Wide Web 25, 1425–1446 (2022). https://doi.org/10.1007/s11280-021-00959-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11280-021-00959-3

Keywords

Search

Navigation