Skip to main content
SpringerLink
Log in

Experimental Evaluation of Selected Approaches to Covariance Matrix Regularization

  • Conference paper
Book cover Artificial Intelligence and Soft Computing (ICAISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9120))

Included in the following conference series:

  • 1893 Accesses

Abstract

Our objective is to asses the performance of covariance matrix regularization methods on real world data, to provide points of reference for future applications. We analyse the following estimators: OAS, Rao-Blackwell-Ledoit-Wolf, Ledoit-Wolf in two versions, and Thresholding on data from several publicly available datasets (K9, Isolet, Slice, Gistette, S1 ADL1). We investigate through several norms the error of estimation from reduced data.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bickel, P.J., Levina, E.: Covariance regularization by thresholding. The Annals of Statistics 36(6), 2577–2604 (2008)

    Article  MathSciNet  Google Scholar 

  2. Bickel, P.J., Levina, E.: Regularized estimation of large covariance matrices. The Annals of Statistics 36(1), 199–227 (2008)

    Article  MathSciNet  Google Scholar 

  3. Chen, Y., Wiesel, A., Eldar, Y.C., Hero, A.O.: Shrinkage algorithms for MMSE covariance estimation. IEEE Transactions on Signal Processing 58(10), 5016–5029 (2010)

    Article  MathSciNet  Google Scholar 

  4. Chiu, T.Y.M., Leonard, T., Tsui, K.W.: The matrix-logarithm covariance model. Journal of American Statistics Assocciation 91, 198–210 (1996)

    Article  MathSciNet  Google Scholar 

  5. Danziger, S.A., Baronio, R., Ho, L., Hall, L., Salmon, K., Hatfield, G.W., Kaiser, P., Lathrop, R.H.: Predicting positive p53 cancer rescue regions using most informative positive (MIP) active learning. PLOS Computational Biology 5(9), 1000498 (2009)

    Google Scholar 

  6. Dey, D.K., Srinivasan, C.: Estimation of a covariance matrix under Stein’s loss. Annals of Statistics 13, 1581–1591 (1985)

    Article  MathSciNet  Google Scholar 

  7. El Karoui, N.: Operator norm consistent estimation of large dimensional sparse covariance matrices. Annals of Statistics 36(6), 2717–2756 (2008)

    Article  MathSciNet  Google Scholar 

  8. Fanty, M., Cole, R.: Spoken letter recognition. Advances in Neural Information Processing Systems 3, 220–226 (1991)

    Google Scholar 

  9. Graf, F., Kriegel, H.-P., Schubert, M., Pölsterl, S., Cavallaro, A.: 2D image registration in CT images using radial image descriptors. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 607–614. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Guyon, I., Gunn, R., Ben-Hur, S.A., Dror, G.: Result analysis of the NIPS 2003 feature selection challenge. Neural Information Processing Systems (2004)

    Google Scholar 

  11. Haff, L.R.: Empirical Bayes estimation of the multivariate normal covariance matrix. Annals of Statistics 8, 586–597 (1980)

    Article  MathSciNet  Google Scholar 

  12. Huang, J.Z., Liu, N., Pourahmadi, M., Liu, L.: Covariance selection and estimation via penalised normal likelihood. Biometrika 93(1), 85–98 (2006)

    Article  MathSciNet  Google Scholar 

  13. Ledoit, O., Wolf, M.: A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis 88(2), 365–411 (2004)

    Article  MathSciNet  Google Scholar 

  14. Leonard, T., Hsu, J.S.J.: Bayesian inference for a covariance matrix. The Annals of Statistics 36, 1669–1696 (1992)

    Article  MathSciNet  Google Scholar 

  15. Pourahmadi, M.: Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation. Biometrika 86, 677–690 (1999)

    Article  MathSciNet  Google Scholar 

  16. Pourahmadi, M.: Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix. Biometrika 87, 425–435 (2000)

    Article  MathSciNet  Google Scholar 

  17. Pourahmadi, M., Wu, W.B.: Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika 90, 831–844 (2003)

    Article  MathSciNet  Google Scholar 

  18. Roggen, D., Calatroni, A., Rossi, M., Holleczek, T., Förster, G., Lukowicz, P., Pirkl, G., Bannach, D., Ferscha, A., Doppler, J., Holzmann, C., Kurz, M., Holl, G., Chavarriaga, R., Sagha, H., Bayati, H., del R. Millán, J.: Collecting complex activity data sets in highly rich networked sensor environments. In: Seventh International Conference on Networked Sensing Systems, INSS 2010 (2010)

    Google Scholar 

  19. Rothman, A.J., Bickel, P.J., Levina, E., Zhu, J.: Sparse permutation invariant covariance estimation. Electronic Journal of Statistics 2, 494–515 (2008)

    Article  MathSciNet  Google Scholar 

  20. Rothman, A.J., Levina, E., Zhu, J.: Sparse estimation of large covariance matrices via nested Lasso penalty. The Annals of Applied Statistics 2, 245–263 (2008)

    Article  MathSciNet  Google Scholar 

  21. Tony Cai, T., Zhang, C.H., Zhou, H.H.: Optimal rates of convergence for covariance matrix estimation. Annals of Statistics 38(4), 2118–2144 (2010)

    Article  MathSciNet  Google Scholar 

  22. Tony Cai, T., Zhou, H.H.: Minimax estimation of large covariance matrices under l1-norm. Statistica Sinica 22, 1319–1378 (2012)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100, Gliwice, Poland

    Przemysław Głomb & Michał Cholewa

Authors
  1. Przemysław Głomb
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michał Cholewa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Leszek Rutkowski

  2. Czestochowa University of Technology, Czestochowa, Poland

    Marcin Korytkowski

  3. Czestochova Univ of Technology, Częstochova, Poland

    Rafal Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. Louisville, Kentucky, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Głomb, P., Cholewa, M. (2015). Experimental Evaluation of Selected Approaches to Covariance Matrix Regularization. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9120. Springer, Cham. https://doi.org/10.1007/978-3-319-19369-4_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19369-4_35

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19368-7

  • Online ISBN: 978-3-319-19369-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation