AISTAT 2017 Paper: A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models
R Lua HTML CSS
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Failed to load latest commit information.
fasjem-cran
17-FASJEM-talk.pdf
README.md
fasjem_g.lua

README.md

References

BibTex Citation:

@InProceedings{pmlr-v54-wang17e,
  title =    {{A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models}},
  author =   {Beilun Wang and Ji Gao and Yanjun Qi},
  booktitle =    {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
  pages =    {1168--1177},
  year =     {2017},
  editor =   {Aarti Singh and Jerry Zhu},
  volume =   {54},
  series =   {Proceedings of Machine Learning Research},
  address =      {Fort Lauderdale, FL, USA},
  month =    {20--22 Apr},
  publisher =    {PMLR},
  pdf =      {http://proceedings.mlr.press/v54/wang17e/wang17e.pdf},
  url =      {http://proceedings.mlr.press/v54/wang17e.html}
}

CRAN R Library page: URL

Context

This repo provides two implementations of the FASJEM algorithm: a novel fast and Scalable approach to estimating multiple sparse Gaussian Graphic Modles (SGGMs) jointly for many related tasks under a high-dimensional situation.

FASJEM is described in the paper A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Model by Beilun Wang, Ji Gao, and Yanjun Qi and accepted by AISTAT 2017. FASJEM has three major contributions:

  • We solve FASJEM through an entry-wise manner which is parallelizable.
  • We choose a proximal algorithm to optimize FASJEM. This improves the computational efficiency from O(Kp3) to O(Kp2) and reduces the memory requirement from O(Kp2) to O(K).
  • We theoretically prove that FASJEM achieves a consistent estimation with a convergence rate of O(log(Kp)/ntot). On several synthetic and four real-world datasets, FASJEM shows significant improvements over baselines on accuracy, computational complexity and memory costs.

implementations

This repo provides two different implementations of the FASJEM algorithm:

  1. the implementation of FASJEM method based on the torch7. To use this GPU version of the FASJEM code, you need to install the torch7 and include the cutorch package.

  2. the R implementation of FASJEM as the R package "fasjem" in CRAN

  • install the R "simule" package through R console:
install.packages('fasjem')
  • then load the library simule in R console, by running:
library(fasjem)
  • then run demo to learn basic functions provided by the fasjem R package, by running:
demo(fasjem)

Contacts

  • bugs, maintenance, feedback, questions: Beilun Wang bw4mw [at] virginia [dot] edu

References

  • ENCODE Project Consortium et al. An integrated encyclopedia of dna elements in the human genome. Nature, 489(7414):57–74, 2012.
  • Trey Ideker and Nevan J Krogan. Differential network biology. Molecular systems biology, 8(1):565, 2012.
  • Tim Beck, Robert K Hastings, Sirisha Gollapudi, Robert C Free, and Anthony J Brookes. Gwas central: a comprehensive resource for the comparison and interrogation of genome-wide association studies. European Journal of Human Genetics, 22(7):949–952, 2014.
  • Steffen L Lauritzen. Graphical models. Oxford University Press, 1996.
  • Kantilal Varichand Mardia, John T Kent, and John M Bibby. Multivariate analysis. 1980.
  • Ming Yuan and Yi Lin. Model selection and estimation in the gaussian graphical model. Biometrika,v94(1):19–35, 2007.
  • Rich Caruana. Multitask learning. Machine learning, 28(1):41–75, 1997.
  • Patrick Danaher, Pei Wang, and Daniela M Witten. The joint graphical lasso for inverse covariance estimation across multiple classes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2013.
  • Karthik Mohan, Palma London, Maryam Fazel, Su-In Lee, and Daniela Witten. Node-based learning of multiple gaussian graphical models. arXiv preprint arXiv:1303.5145, 2013.
  • Julien Chiquet, Yves Grandvalet, and Christophe Ambroise. Inferring multiple graphical structures. Statistics and Computing, 21(4):537–553, 2011.
  • Jean Honorio and Dimitris Samaras. Multi-task learning of gaussian graphical models. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), pages 447–454, 2010.
  • Jian Guo, Elizaveta Levina, George Michailidis, and Ji Zhu. Joint estimation of multiple graphical models. Biometrika, page asq060, 2011.
  • Bai Zhang and Yue Wang. Learning structural changes of gaussian graphical models in controlled experiments. arXiv preprint arXiv:1203.3532, 2012.
  • Yi Zhang and Jeff G Schneider. Learning multiple tasks with a sparse matrix-normal penalty. In Advances in Neural Information Processing Systems, pages 2550–2558, 2010.
  • Yunzhang Zhu, Xiaotong Shen, and Wei Pan. Structural pursuit over multiple undirected graphs. Journal of the American Statistical Association, 109(508):1683–1696, 2014.
  • Eunho Yang, Aurélie C Lozano, and Pradeep K Ravikumar. Elementary estimators for graphical models. In Advances in Neural Information Processing Systems, pages 2159–2167, 2014.
  • Onureena Banerjee, Laurent El Ghaoui, and Alexandre d’Aspremont. Model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data. The Journal of Machine Learning Research, 9:485–516, 2008.
  • Sahand Negahban, Bin Yu, Martin J Wainwright, and Pradeep K Ravikumar. A unified framework for high-dimensional analysis of m-estimators with decomposable regularizers. In Advances in Neural Information Processing Systems, pages 1348–1356, 2009.
  • Eunho Yang, Aurelie Lozano, and Pradeep Ravikumar. Elementary estimators for high-dimensional linear regression. In Proceedings of the 31st International Conference on Machine Learning (ICML-14), pages 388–396, 2014.
  • Eunho Yang, Aurelie C Lozano, and Pradeep D Ravikumar. Elementary estimators for sparse covariance matrices and other structured moments. In ICML, pages 397–405, 2014.
  • Eunho Yang and Pradeep K Ravikumar. Dirty statistical models. In Advances in Neural Information Processing Systems, pages 611–619, 2013.
  • Patrick L Combettes and Jean-Christophe Pesquet. Proximal splitting methods in signal processing. A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models In Fixed-point algorithms for inverse problems in science and engineering, pages 185–212. Springer, 2011.
  • John Nickolls, Ian Buck, Michael Garland, and Kevin Skadron. Scalable parallel programming with cuda. Queue, 6(2):40–53, 2008.
  • Trevor Hastie, Robert Tibshirani, Jerome Friedman, T Hastie, J Friedman, and R Tibshirani. The elements of statistical learning, volume 2. Springer, 2009.
  • Adam J Rothman, Peter J Bickel, Elizaveta Levina, Ji Zhu, et al. Sparse permutation invariant covariance estimation. Electronic Journal of Statistics, 2:494 \ – 515, 2008.
  • Tony Cai, Weidong Liu, and Xi Luo. A constrained l1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 106(494):594–607, 2011.
  • Cho-Jui Hsieh, Matyas A Sustik, Inderjit S Dhillon, and Pradeep D Ravikumar. Sparse inverse covariance matrix estimation using quadratic approximation. In NIPS, pages 2330–2338, 2011.
  • Peter J Bickel and Elizaveta Levina. Covariance regularization by thresholding. The Annals of Statistics, pages 2577–2604, 2008.
  • Ronan Collobert, Koray Kavukcuoglu, and Clé-ment Farabet. Torch7: A matlab-like environmentfor machine learning. In BigLearn, NIPS Workshop,number EPFL-CONF-192376, 2011.