Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso

References

• Ahmed, A., and Xing, E. P. (2009), “Recovering Time-Varying Networks of Dependencies in Social and Biological Studies,” Proceedings of the National Academy of Sciences of the United States of America, 106, 11878–11883.
   PubMed Web of Science ®Google Scholar
• Alaíz, C. M., Barbero, A., and Dorronsoro, J. R. (2013), “Group Fused Lasso,” in Artificial Neural Networks and Machine Learning—ICANN 2013, pp. 66–73.
   Google Scholar
• Angelosante, D., and Giannakis, G. B. (2011), “Sparse Graphical Modeling of Piecewise-Stationary Time Series,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1960–1963.
   Google Scholar
• Arbeitman, M. N., Furlong, E. E. M., Imam, F., Johnson, E., Null, B. H., Baker, B. S., Krasnow, M. A., Scott, M. P., Davis, R. W., and White, K. P. (2002), “Gene Expression During the Life Cycle of Drosophila Melanogaster,” Science, 297, 2270–2275.
   PubMed Web of Science ®Google Scholar
• Attrill, H., Falls, K., Goodman, J. L., Millburn, G. H., Antonazzo, G., Rey, A. J., and Marygold, S. J. (2016), “FlyBase: Establishing a Gene Group Resource for Drosophila Melanogaster,” Nucleic Acids Research, 44, D786–D792.
   PubMed Web of Science ®Google Scholar
• Banerjee, O., El Ghaoui, L., and D’Aspremont, A. (2008), “Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data,” The Journal of Machine Learning Research, 9, 485–516.
   Web of Science ®Google Scholar
• Bleakley, K., and Vert, J.-P. (2011), “The group fused Lasso for multiple change-point detection,” https://hal.archives-ouvertes.fr/hal-00602121, working paper or preprint, https://hal.archives-ouvertes.fr/hal-00602121/file/techreport.pdf, hal-00602121, v1.
   Google Scholar
• Boyd, S., Parikh, N., and Chu, E. (2011), “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Foundations and Trends in Machine Learning, 3, 1–122.
   Google Scholar
• Chun, H., Zhang, X., and Zhao, H. (2014), “Gene Regulation Network Inference With Joint Sparse Gaussian Graphical Models,” Journal of Computational and Graphical Statistics, 24, 954–974.
   PubMed Web of Science ®Google Scholar
• Combettes, P. L., and Pesquet, J. C. (2011), “Proximal Splitting Methods in Signal Processing,” Fixed-Point Algorithms for Inverse Problems for InverseProblems in Science and Engineering, 49, 185–212.
   Google Scholar
• Danaher, P., Wang, P., and Witten, D. M. (2013), “The Joint Graphical Lasso for Inverse Covariance Estimation Across Multiple Classes,” Journal of theRoyal Statistical Society, Series B, 76, 373–397.
   Google Scholar
• Drton, M., and Perlman, M. D. (2004), “Model Selection for Gaussian Concentration Graphs,” Biometrika, 91, 591–602.
   Web of Science ®Google Scholar
• Eckstein, J., and Bertsekas, D. P. (1992), “On the Douglas-Rachford Splitting Method and the Proximal Point Algorithm for Maximal Monotone Operators,” Mathematical Programming, 55, 293–318.
   Web of Science ®Google Scholar
• Forslund, K., Pekkari, I., and Sonnhammer, E. L. (2011), “Domain ArchitectureConservation in Orthologs,” BMC Bioinformatics, 12, 326.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., Hoefling, H., and Tibshirani, R. (2007), “Pathwise Coordinate Optimization,” Annals of Applied Statistics, 9, 432–441.
   Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2008), “Sparse Inverse Covariance Estimation With the Graphical Lasso,” Biostatistics (Oxford, England), 9, 432–441.
   PubMed Web of Science ®Google Scholar
• Gibberd, A. J., and Nelson, J. D. B. (2014), “High Dimensional Changepoint Detection With a Dynamic Graphical Lasso,” in IEEE International Conferenceon Acoustics, Speech and Signal Processing (ICASSP), pp. 2684–2688.
   Google Scholar
• Glowinski, R., and Le Tallec, P. (1989), Augmented Lagrangian and Operator-SplittingMethods in Nonlinear Mechanics, Philadelphia: SIAM.
   Google Scholar
• Harchaoui, Z., and Lévy-Leduc, C. (2010), “Multiple Change-Point Estimation With a Total Variation Penalty,” Journal of the American Statistical Association, 105, 1480–1493.
   Web of Science ®Google Scholar
• Kolar, M., and Xing, E. P. (2011), “On Time Varying Undirected Graphs,” in Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) (Vol. 15), pp. 407–415.
   Google Scholar
• ——— (2012), “Estimating Networks With Jumps,” Electronic Journal of Statistics, 6, 2069–2106.
   PubMed Web of Science ®Google Scholar
• Lafferty, J., Liu, H., and Wasserman, L. (2012), “Sparse Nonparametric Graphical Models,” Statistical Science, 27, 519–537.
   Web of Science ®Google Scholar
• Lauritzen, S. L. (1996), Graphical Models, Oxford: Oxford University Press.
   Google Scholar
• Lèbre, S., Becq, J., Devaux, F., Stumpf, M. P. H., and Lelandais, G. (2010), “Statistical Inference of the Time-Varying Structureof Gene-Regulation Networks,” BMC Systems Biology, 4, 130.
   PubMed Web of Science ®Google Scholar
• Lee, J. D., and Hastie, T. J. (2015), “Learning the Structure of Mixed Graphical Models,” Journal of Computational and Graphical Statistics, 24, 230–253.
   PubMed Web of Science ®Google Scholar
• Liu, J., Yuan, L., and Ye, J. (2010), “An Efficient Algorithm for a Class of Fused Lasso Problems,” in Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 323–332.
   Google Scholar
• Monti, R. P., Hellyer, P., Sharp, D., Leech, R., Anagnostopoulos, C., and Montana, G. (2014), “Estimating Time-Varying Brain Connectivity Networks from Functional MRI Time Series,” NeuroImage, 103, 427–443.
   PubMed Web of Science ®Google Scholar
• Parikh, N., and Boyd, S. (2013), “Proximal Algorithms,” Foundations and Trends in Optimization, 1, 123–231.
   Google Scholar
• Ravikumar, P., Wainwright, M. J., Raskutti, G., and Yu, B. (2011), “High-Dimensional Covariance Estimation by Minimizing l1-Penalized Log-Determinant Divergence,” Electronic Journal of Statistics, 5, 935–980.
   Web of Science ®Google Scholar
• Roy, S., Atchadé, Y., and Michailidis, G. (2016), “Change Point Estimation in High Dimensional Markov Random-Field Models,” Journal of the Royal Statistical Society, Series B, 1467–9868, https://doi.org/10.1111/rssb.12205, 10.1111/rssb.12205.
   Google Scholar
• Simon, N., Friedman, J., Hastie, T., and Tibshirani, R. (2013), “A Sparse-Group Lasso,” Journal of Computational and Graphical Statistics, 22, 231–245.
   Web of Science ®Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage andSelection via the Lasso,” Journal of the Royal Statistical Society, Series B, 267–288.
   Google Scholar
• Tseng, P., and Yun, S. (2009), “A Coordinate Gradient DescentMethod for Nonsmooth Separable Minimization,” Mathematical Programming, 117, 387–423.
   Web of Science ®Google Scholar
• Wang, H. (2012), “Bayesian Graphical Lasso Models and Efficient Posterior Computation,” Bayesian Analysis, 7, 867–886.
   Web of Science ®Google Scholar
• Yang, S., Lu, Z., Shen, X., Wonka, P., and Ye, J. (2015). “Fused MultipleGraphical Lasso,” SIAM Journal on Optimization, 25, 916–943.
   Web of Science ®Google Scholar
• Yuan, M., and Lin, Y. (2006), “Model Selection and Estimationin Regression With Grouped Variables,” Journal of the Royal Statistical Society, 68, 49–67.
   Google Scholar
• Yuan, X. (2011), “Alternating Direction Method for Covariance Selection Models,” Journal of Scientific Computing, 51, 261– 273.
   Web of Science ®Google Scholar
• Zhang, B., Geng, J., and Lai, L. (2014), “Multiple Change-Points Estimation in Linear Regression Models via Sparse Group Lasso,” IEEE Transactionson Signal Processing, 63, 2209–2224.
   Web of Science ®Google Scholar
• Zhou, S., Lafferty, J., and Wasserman, L. (2012), “Time Varying Undirected Graphs,” Machine Learning, 80, 295–319.
   Web of Science ®Google Scholar