Exact hybrid covariance thresholding for joint graphical lasso

Qingming Tang; Chao Yang; Jian Peng; Jinbo Xu

doi:10.1007/978-3-319-23525-7_36

Exact hybrid covariance thresholding for joint graphical lasso

Qingming Tang, Chao Yang, Jian Peng, Jinbo Xu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper studies precision matrix estimation for multiple related Gaussian graphical models from a dataset consisting of different classes, based upon the formulation of this problem as group graphical lasso. In particular, this paper proposes a novel hybrid covariance thresholding algorithm that can effectively identify zero entries in the precision matrices and split a large joint graphical lasso problem into many small subproblems. Our hybrid covariance thresholding method is superior to existing uniform thresholding methods in that our method can split the precision matrix of each individual class using different partition schemes and thus, split group graphical lasso into much smaller subproblems, each of which can be solved very fast. This paper also establishes necessary and sufficient conditions for our hybrid covariance thresholding algorithm. Experimental results on both synthetic and real data validate the superior performance of our thresholding method over the others.

Original language	English (US)
Title of host publication	Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2015
Editors	Vitor Santos Costa, Carlos Soares, Annalisa Appice, Annalisa Appice, Pedro Pereira Rodrigues, Vitor Santos Costa, Carlos Soares, João Gama, Alípio Jorge, Pedro Pereira Rodrigues, João Gama, Vitor Santos Costa, Alípio Jorge, Annalisa Appice, Pedro Pereira Rodrigues, João Gama, Annalisa Appice, Carlos Soares, Alípio Jorge, João Gama, Pedro Pereira Rodrigues, Vitor Santos Costa, Carlos Soares, Alípio Jorge
Publisher	Springer
Pages	593-607
Number of pages	15
ISBN (Print)	9783319235240, 9783319235240, 9783319235240, 9783319235240
DOIs	https://doi.org/10.1007/978-3-319-23525-7_36
State	Published - 2015
Event	European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2015 - Porto, Portugal Duration: Sep 7 2015 → Sep 11 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9285
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2015
Country/Territory	Portugal
City	Porto
Period	9/7/15 → 9/11/15

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Online availability

10.1007/978-3-319-23525-7_36

Library availability

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Tang, Q., Yang, C., Peng, J., & Xu, J. (2015). Exact hybrid covariance thresholding for joint graphical lasso. In V. S. Costa, C. Soares, A. Appice, A. Appice, P. P. Rodrigues, V. S. Costa, C. Soares, J. Gama, A. Jorge, P. P. Rodrigues, J. Gama, V. S. Costa, A. Jorge, A. Appice, P. P. Rodrigues, J. Gama, A. Appice, C. Soares, A. Jorge, J. Gama, P. P. Rodrigues, V. S. Costa, C. Soares, ... A. Jorge (Eds.), Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2015 (pp. 593-607). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9285). Springer. https://doi.org/10.1007/978-3-319-23525-7_36

Exact hybrid covariance thresholding for joint graphical lasso. / Tang, Qingming; Yang, Chao; Peng, Jian et al.
Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2015. ed. / Vitor Santos Costa; Carlos Soares; Annalisa Appice; Annalisa Appice; Pedro Pereira Rodrigues; Vitor Santos Costa; Carlos Soares; João Gama; Alípio Jorge; Pedro Pereira Rodrigues; João Gama; Vitor Santos Costa; Alípio Jorge; Annalisa Appice; Pedro Pereira Rodrigues; João Gama; Annalisa Appice; Carlos Soares; Alípio Jorge; João Gama; Pedro Pereira Rodrigues; Vitor Santos Costa; Carlos Soares; Alípio Jorge. Springer, 2015. p. 593-607 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9285).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Tang, Q, Yang, C, Peng, J & Xu, J 2015, Exact hybrid covariance thresholding for joint graphical lasso. in VS Costa, C Soares, A Appice, A Appice, PP Rodrigues, VS Costa, C Soares, J Gama, A Jorge, PP Rodrigues, J Gama, VS Costa, A Jorge, A Appice, PP Rodrigues, J Gama, A Appice, C Soares, A Jorge, J Gama, PP Rodrigues, VS Costa, C Soares & A Jorge (eds), Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2015. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9285, Springer, pp. 593-607, European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2015, Porto, Portugal, 9/7/15. https://doi.org/10.1007/978-3-319-23525-7_36

Tang Q, Yang C, Peng J, Xu J. Exact hybrid covariance thresholding for joint graphical lasso. In Costa VS, Soares C, Appice A, Appice A, Rodrigues PP, Costa VS, Soares C, Gama J, Jorge A, Rodrigues PP, Gama J, Costa VS, Jorge A, Appice A, Rodrigues PP, Gama J, Appice A, Soares C, Jorge A, Gama J, Rodrigues PP, Costa VS, Soares C, Jorge A, editors, Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2015. Springer. 2015. p. 593-607. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-23525-7_36

Tang, Qingming ; Yang, Chao ; Peng, Jian et al. / Exact hybrid covariance thresholding for joint graphical lasso. Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2015. editor / Vitor Santos Costa ; Carlos Soares ; Annalisa Appice ; Annalisa Appice ; Pedro Pereira Rodrigues ; Vitor Santos Costa ; Carlos Soares ; João Gama ; Alípio Jorge ; Pedro Pereira Rodrigues ; João Gama ; Vitor Santos Costa ; Alípio Jorge ; Annalisa Appice ; Pedro Pereira Rodrigues ; João Gama ; Annalisa Appice ; Carlos Soares ; Alípio Jorge ; João Gama ; Pedro Pereira Rodrigues ; Vitor Santos Costa ; Carlos Soares ; Alípio Jorge. Springer, 2015. pp. 593-607 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Exact hybrid covariance thresholding for joint graphical lasso

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