×
Tsai, Katherine; Koyejo, Oluwasanmi; Kolar, Mladen

Joint Gaussian graphical model estimation: a survey. (English) Zbl 07910990

Wiley Interdiscip. Rev., WIREs Comput. Stat. 14, No. 6, Article ID e1582, 24 p. (2022).

Cited in 1 Document

MSC:

62-08 Computational methods for problems pertaining to statistics

Keywords:

Gaussian graphical model; graphical lasso; high-dimensional estimation; joint network; sparsity
Cite Review PDF
Full Text: DOI arXiv
OA License

References:

[1] Abreu, R., Leal, A., & Figueiredo, P. (2018). Eeg‐informed fmri: A review of data analysis methods. Frontiers in Human Neuroscience, 12, 29.
[2] Andersen, M., Winther, O., Hansen, L. K., Poldrack, R., & Koyejo, O. (2018). Bayesian structure learning for dynamic brain connectivity. In Proceedings of the twenty‐first international conference on artificial intelligence and statistics, pp. 1436-1446.
[3] Atay‐Kayis, A., & Massam, H. (2005). A Monte Carlo method for computing the marginal likelihood in nondecomposable gaussian graphical models. Biometrika, 92(2), 317-335. · Zbl 1094.62028
[4] Barber, R. F., & Kolar, M. (2018). Rocket: Robust confidence intervals via kendall’s tau for transelliptical graphical models. The Annals of Statistics, 46(6), 3422-3450. · Zbl 1410.62059
[5] Belilovsky, E., Varoquaux, G., & Blaschko, M. B. (2016). Testing for differences in Gaussian graphical models: Applications to brain connectivity. In Advances in neural information processing systems, volume 29, pp. 595-603.
[6] Bilgrau, A. E., Peeters, C. F., Eriksen, P. S., Bøgsted, M., & vanWieringen, W. N. (2020). Targeted fused ridge estimation of inverse covariance matrices from multiple high‐dimensional data classes. Journal of Machine Learning Research, 21(26), 1-52. · Zbl 1499.62177
[7] Bühlmann, P., & van deGeer, S. (2011). Statistics for high‐dimensional data: Methods, theory and applications. Springer Science & Business Media. · Zbl 1273.62015
[8] Cai, T., Liu, W., & Luo, X. (2011). A constrained ℓ_1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 106(494), 594-607. · Zbl 1232.62087
[9] Calhoun, V. D., Miller, R., Pearlson, G., & Adali, T. (2014). The chronnectome: Time‐varying connectivity networks as the next frontier in fmri data discovery. Neuron, 84(2), 262-274.
[10] Chan, T. E., Stumpf, M. P., & Babtie, A. C. (2017). Gene regulatory network inference from single‐cell data using multivariate information measures. Cell Systems, 5(3), 251-267.
[11] Chandrasekaran, V., Parrilo, P. A., & Willsky, A. S. (2012). Latent variable graphical model selection via convex optimization. The Annals of Statistics, 40(4), 1935-1967. · Zbl 1257.62061
[12] Chiquet, J., Grandvalet, Y., & Ambroise, C. (2011). Inferring multiple graphical structures. Statistics and Computing, 21(4), 537-553. · Zbl 1221.62085
[13] Chun, H., Zhang, X., & Zhao, H. (2015). Gene regulation network inference with joint sparse Gaussian graphical models. Journal of Computational and Graphical Statistics, 24(4), 954-974.
[14] Colclough, G. L., Woolrich, M. W., Harrison, S. J., López, P. A. R., Valdes‐Sosa, P. A., & Smith, S. M. (2018). Multi‐subject hierarchical inverse covariance modelling improves estimation of functional brain networks. NeuroImage, 178, 370-384.
[15] Danaher, P., Wang, P., & Witten, D. M. (2014). The joint graphical lasso for inverse covariance estimation across multiple classes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(2), 373-397. · Zbl 07555455
[16] Dobra, A., Hans, C., Jones, B., Nevins, J. R., Yao, G., & West, M. (2004). Sparse graphical models for exploring gene expression data. Journal of Multivariate Analysis, 90(1), 196-212. · Zbl 1047.62104
[17] Dondelinger, F., Lèbre, S., & Husmeier, D. (2013). Non‐homogeneous dynamic Bayesian networks with Bayesian regularization for inferring gene regulatory networks with gradually time‐varying structure. Machine Learning, 90(2), 191-230. · Zbl 1260.92027
[18] Drton, M. (2009). Discrete chain graph models. Bernoulli, 15(3), 736-753. · Zbl 1452.62348
[19] Drton, M., & Maathuis, M. H. (2017). Structure learning in graphical modeling. Annual Review of Statistics and Its Application, 4(1), 365-393.
[20] Drton, M., & Perlman, M. D. (2004). Model selection for Gaussian concentration graphs. Biometrika, 91(3), 591-602. · Zbl 1108.62098
[21] Drton, M., & Richardson, T. S. (2008). Binary models for marginal independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(2), 287-309. · Zbl 1148.62043
[22] Felsenstein, J. (1981). Evolutionary trees from dna sequences: A maximum likelihood approach. Journal of Molecular Evolution, 17(6), 368-376.
[23] Foti, N. J., & Fox, E. B. (2019). Statistical model‐based approaches for functional connectivity analysis of neuroimaging data. Current Opinion in Neurobiology, 55, 48-54.
[24] Friedman, N., Linial, M., Nachman, I., & Pe’er, D. (2000). Using Bayesian networks to analyze expression data. Journal of Computational Biology, 7, 601-620.
[25] Gan, L., Yang, X., Nariestty, N. N., & Liang, F. (2019). Bayesian joint estimation of multiple graphical models. In Proceedings of the conference on neural information processing systems.
[26] Gibberd, A. J., & Nelson, J. D. (2017). Regularized estimation of piecewise constant Gaussian graphical models: The group‐fused graphical lasso. Journal of Computational and Graphical Statistics, 26(3), 623-634.
[27] Gonzalez‐Castillo, J., & Bandettini, P. A. (2018). Task‐based dynamic functional connectivity: Recent findings and open questions. NeuroImage, 180, 526-533.
[28] Greenewald, K., Park, S., Zhou, S., & Giessing, A. (2017). Time‐dependent spatially varying graphical models, with application to brain fmri data analysis. In Advances in neural information processing systems, volume 30, pp. 5832-5840.
[29] Guo, J., Levina, E., Michailidis, G., & Zhu, J. (2011). Joint estimation of multiple graphical models. Biometrika, 98(1), 1-15. · Zbl 1214.62058
[30] Hallac, D., Park, Y., Boyd, S., & Leskovec, J. (2017). Network inference via the time‐varying graphical lasso. In Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining, pp. 205-213.
[31] Hao, B., Sun, W. W., Liu, Y., & Cheng, G. (2018). Simultaneous clustering and estimation of heterogeneous graphical models. Journal of Machine Learning Research, 18, 217-211. · Zbl 1473.62220
[32] Hsieh, C.‐J., Sustik, M. A., Dhillon, I. S., Ravikumar, P. K., & Poldrack, R. (2013). Big & quic: Sparse inverse covariance estimation for a million variables. In Advances in neural information processing systems, volume 26, pp. 3165-3173.
[33] Huster, R. J., Debener, S., Eichele, T., & Herrmann, C. S. (2012). Methods for simultaneous eeg‐fmri: An introductory review. Journal of Neuroscience, 32(18), 6053-6060.
[34] Janková, J., & van deGeer, S. (2015). Confidence intervals for high‐dimensional inverse covariance estimation. Electronic Journal of Statistics, 9(1), 1205-1229. · Zbl 1328.62458
[35] Janková, J., & van deGeer, S. A. (2017). Honest confidence regions and optimality in high‐dimensional precision matrix estimation. TEST, 26(1), 143-162. · Zbl 1368.62204
[36] Kim, B., Liu, S., & Kolar, M. (2021). Two‐sample inference for high‐dimensional markov networks. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 83(5), 939-962. · Zbl 07555287
[37] Kling, T., Johansson, P., Sanchez, J., Marinescu, V. D., Jörnsten, R., & Nelander, S. (2015). Efficient exploration of pan‐cancer networks by generalized covariance selection and interactive web content. Nucleic Acids Research, 43(15), e98.
[38] Kolar, M., Song, L., Ahmed, A., & Xing, E. P. (2010). Estimating time‐varying networks. The Annals of Applied Statistics, 4, 94-123. · Zbl 1189.62142
[39] Kolar, M., & Xing, E. P. (2012). Estimating networks with jumps. Electronic Journal of Statistics, 6, 2069-2106. · Zbl 1295.62032
[40] Lauritzen, S. L. (1996). Graphical models. Clarendon Press. · Zbl 0907.62001
[41] Lee, W., & Liu, Y. (2015). Joint estimation of multiple precision matrices with common structures. The Journal of Machine Learning Research, 16(1), 1035-1062. · Zbl 1360.62274
[42] Lenkoski, A., & Dobra, A. (2011). Computational aspects related to inference in Gaussian graphical models with the g‐wishart prior. Journal of Computational and Graphical Statistics, 20(1), 140-157.
[43] Li, Q., & Li, L. (2021). Integrative factor regression and its inference for multimodal data analysis. Journal of the American Statistical Association, 1-15. doi:10.1080/01621459.2021.1914635
[44] Li, Z., Mccormick, T., & Clark, S. (2019). Bayesian joint spike‐and‐slab graphical lasso. In Proceedings of the 36th international conference on machine learning, volume 97 of proceedings of machine learning research, pp. 3877-3885.
[45] Lin, Z., Wang, T., Yang, C., & Zhao, H. (2017). On joint estimation of Gaussian graphical models for spatial and temporal data. Biometrics, 73(3), 769-779. · Zbl 1522.62179
[46] Liu, H., Han, F., Yuan, M., Lafferty, J., & Wasserman, L. (2012). High‐dimensional semiparametric Gaussian copula graphical models. The Annals of Statistics, 40(4), 2293-2326. · Zbl 1297.62073
[47] Liu, W. (2017). Structural similarity and difference testing on multiple sparse Gaussian graphical models. The Annals of Statistics, 45(6), 2680-2707. · Zbl 1486.62178
[48] Lock, E. F., Hoadley, K. A., Marron, J. S., & Nobel, A. B. (2013). Joint and individual variation explained (jive) for integrated analysis of multiple data types. The Annals of Applied Statistics, 7(1), 523-542. · Zbl 1454.62355
[49] Lu, J., Kolar, M., & Liu, H. (2018). Post‐regularization inference for time‐varying nonparanormal graphical models. Journal of Machine Learning Research, 18(203), 1-78. · Zbl 1473.62198
[50] Lukemire, J., Kundu, S., Pagnoni, G., & Guo, Y. (2021). Bayesian joint modeling of multiple brain functional networks. Journal of the American Statistical Association, 116(534), 518-530. · Zbl 1464.62460
[51] Lurie, D. J., Kessler, D., Bassett, D. S., Betzel, R. F., Breakspear, M., Kheilholz, S., Kucyi, A., Liégeois, R., Lindquist, M. A., McIntosh, A. R., Poldrack, R. A., Shine, J. M., Thompson, W. H., Bielczyk, N. Z., Douw, L., Kraft, D., Miller, R. L., Muthuraman, M., Pasquini, L., … Calhoun, V. D. (2020). Questions and controversies in the study of time‐varying functional connectivity in resting fmri. Network Neuroscience, 4(1), 30-69.
[52] Ma, J., & Michailidis, G. (2016). Joint structural estimation of multiple graphical models. The Journal of Machine Learning Research, 17(1), 5777-5824. · Zbl 1392.62198
[53] Maathuis, M., Drton, M., Lauritzen, S., & Wainwright, M. (2018). Handbook of graphical models. CRC Press.
[54] Manning, J. R., Zhu, X., Willke, T. L., Ranganath, R., Stachenfeld, K., Hasson, U., Blei, D. M., & Norman, K. A. (2018). A probabilistic approach to discovering dynamic full‐brain functional connectivity patterns. NeuroImage, 180, 243-252.
[55] Marlin, B. M., & Murphy, K. P. (2009). Sparse Gaussian graphical models with unknown block structure. In Proceedings of the 26th annual international conference on machine learning, pp. 705-712.
[56] Meinshausen, N., & Bühlmann, P. (2006). High‐dimensional graphs and variable selection with the lasso. The Annals of Statistics, 34(3), 1436-1462. · Zbl 1113.62082
[57] Mitchell, T. J., & Beauchamp, J. J. (1988). Bayesian variable selection in linear regression. Journal of the American Statistical Association, 83(404), 1023-1032. · Zbl 0673.62051
[58] Mitra, R., Müller, P., & Ji, Y. (2016). Bayesian graphical models for differential pathways. Bayesian Analysis, 11(1), 99-124. · Zbl 1359.62282
[59] Mohammadi, A., & Wit, E. C. (2015). Bayesian structure learning in sparse Gaussian graphical models. Bayesian Analysis, 10(1), 109-138. · Zbl 1335.62056
[60] Mohan, K., Chung, M., Han, S., Witten, D., Lee, S.‐I., & Fazel, M. (2012). Structured learning of Gaussian graphical models. In Advances in neural information processing systems, volume 25, pp. 620-628.
[61] Mohan, K., London, P., Fazel, M., Witten, D., & Lee, S.‐I. (2014). Node‐based learning of multiple Gaussian graphical models. The Journal of Machine Learning Research, 15(1), 445-488. · Zbl 1318.62181
[62] Monti, R. P., Hellyer, P., Sharp, D., Leech, R., Anagnostopoulos, C., & Montana, G. (2014). Estimating time‐varying brain connectivity networks from functional mri time series. NeuroImage, 103, 427-443.
[63] Na, S., Kolar, M., & Koyejo, O. (2021). Estimating differential latent variable graphical models with applications to brain connectivity. Biometrika, 108(2), 425-442. · Zbl 07458264
[64] Oates, C., & Mukherjee, S. (2014). Joint structure learning of multiple non‐exchangeable networks. In Proceedings of the seventeenth international conference on artificial intelligence and statistics, volume 33, pp. 687-695.
[65] Pan, W., & Shen, X. (2007). Penalized model‐based clustering with application to variable selection. Journal of Machine Learning Research, 8(41), 1145-1164. · Zbl 1222.68279
[66] Peterson, C., Stingo, F. C., & Vannucci, M. (2015). Bayesian inference of multiple Gaussian graphical models. Journal of the American Statistical Association, 110(509), 159-174. · Zbl 1373.62106
[67] Pierson, E., Consortium, G., Koller, D., Battle, A., & Mostafavi, S. (2015). Sharing and specificity of co‐expression networks across 35 human tissues. PLoS Computational Biology, 11(5), e1004220.
[68] Poldrack, R. A., Mumford, J. A., & Nichols, T. E. (2011). Handbook of functional MRI data analysis. Cambridge University Press. · Zbl 1321.92015
[69] Price, B. S., Molstad, A. J., & Sherwood, B. (2021). Estimating multiple precision matrices with cluster fusion regularization. Journal of Computational and Graphical Statistics, 30, 1-12. · Zbl 07499920
[70] Qiu, H., Han, F., Liu, H., & Caffo, B. (2016). Joint estimation of multiple graphical models from high dimensional time series. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(2), 487-504. · Zbl 1414.62379
[71] Ren, Z., Sun, T., Zhang, C.‐H., & Zhou, H. H. (2015). Asymptotic normality and optimalities in estimation of large Gaussian graphical models. The Annals of Statistics, 43(3), 991-1026. · Zbl 1328.62342
[72] Roverato, A. (2002). Hyper inverse wishart distribution for non‐decomposable graphs and its application to Bayesian inference for Gaussian graphical models. Scandinavian Journal of Statistics, 29(3), 391-411. · Zbl 1036.62027
[73] Saegusa, T., & Shojaie, A. (2016). Joint estimation of precision matrices in heterogeneous populations. Electronic journal of statistics, 10(1), 1341-1392. · Zbl 1341.62130
[74] Schäfer, J., & Strimmer, K. (2005). A shrinkage approach to large‐scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4(1), 32.
[75] Schwab, S., Harbord, R., Zerbi, V., Elliott, L., Afyouni, S., Smith, J. Q., Woolrich, M. W., Smith, S. M., & Nichols, T. E. (2018). Directed functional connectivity using dynamic graphical models. NeuroImage, 175, 340-353.
[76] Shaddox, E., Peterson, C. B., Stingo, F. C., Hanania, N. A., Cruickshank‐Quinn, C., Kechris, K., Bowler, R., & Vannucci, M. (2020). Bayesian inference of networks across multiple sample groups and data types. Biostatistics, 21(3), 561-576.
[77] Shaddox, E., Stingo, F. C., Peterson, C. B., Jacobson, S., Cruickshank‐Quinn, C., Kechris, K., Bowler, R., & Vannucci, M. (2018). A Bayesian approach for learning gene networks underlying disease severity in copd. Statistics in Biosciences, 10(1), 59-85.
[78] Shan, L., & Kim, I. (2018). Joint estimation of multiple Gaussian graphical models across unbalanced classes. Computational Statistics & Data Analysis, 121, 89-103. · Zbl 1469.62140
[79] Shan, L., Qiao, Z., Cheng, L., & Kim, I. (2020). Joint estimation of the two‐level Gaussian graphical models across multiple classes. Journal of Computational and Graphical Statistics, 29(3), 562-579. · Zbl 07499297
[80] Shine, J. M., Bissett, P. G., Bell, P. T., Koyejo, O., Balsters, J. H., Gorgolewski, K. J., Moodie, C. A., & Poldrack, R. A. (2016). The dynamics of functional brain networks: Integrated network states during cognitive task performance. Neuron, 92(2), 544-554.
[81] Shojaie, A. (2021). Differential network analysis: A statistical perspective. Wiley Interdisciplinary Reviews: Computational Statistics, 13(2), e1508. · Zbl 07910733
[82] Skripnikov, A., & Michailidis, G. (2019). Regularized joint estimation of related vector autoregressive models. Computational Statistics & Data Analysis, 139, 164-177. · Zbl 1507.62158
[83] Sun, S., Kolar, M., & Xu, J. (2015). Learning structured densities via infinite dimensional exponential families. In Advances in neural information processing systems, volume 28, pp. 2287-2295.
[84] Sun, W., Wang, J., & Fang, Y. (2012). Regularized k‐means clustering of high‐dimensional data and its asymptotic consistency. Electronic Journal of Statistics, 6, 148-167. · Zbl 1335.62109
[85] Tan, L. S., Jasra, A., De Iorio, M., & Ebbels, T. M. (2017). Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks. The Annals of Applied Statistics, 11(4), 2222-2251. · Zbl 1383.62294
[86] Varoquaux, G., Baronnet, F., Kleinschmidt, A., Fillard, P., & Thirion, B. (2010). Detection of brain functional‐connectivity difference in post‐stroke patients using group‐level covariance modeling. In International conference on medical image computing and computer‐assisted intervention, pp. 200-208.
[87] Wang, H. (2012). Bayesian graphical lasso models and efficient posterior computation. Bayesian Analysis, 7(4), 867-886. · Zbl 1330.62041
[88] Wang, J., & Kolar, M. (2014). Inference for sparse conditional precision matrices. arXiv Preprint, 1412, 7638.
[89] Wang, J., & Kolar, M. (2016). Inference for high‐dimensional exponential family graphical models. In A.Gretton (ed.) & C. C.Robert (ed.) (Eds.), Proceedings of the 19th international conference on artificial intelligence and statistics, volume 51 of proceedings of machine learning research (pp. 1042-1050). PMLR.
[90] Wang, X., Kolar, M., & Shojaie, A. (2020). Statistical inference for networks of high‐dimensional point processes. arXiv Preprint.
[91] Wang, X., & Shojaie, A. (2021). Joint estimation and inference for multi‐experiment networks of high‐dimensional point processes. arXiv Preprint.
[92] Wang, Y., Ma, J., & Shojaie, A. (2021). Direct estimation of differential granger causality between two high‐dimensional time series. arXiv Preprint.
[93] Xia, Y., Cai, T., & Cai, T. T. (2015). Testing differential networks with applications to the detection of gene‐gene interactions. Biometrika, 102(2), 247-266. · Zbl 1452.62392
[94] Xu, P., & Gu, Q. (2016). Semiparametric differential graph models. In D.Lee (ed.), M.Sugiyama (ed.), U.Luxburg (ed.), I.Guyon (ed.), & R.Garnett (ed.) (Eds.), Advances in neural information processing systems (pp. 1064-1072). Curran Associates, Inc.
[95] Yajima, M., Telesca, D., Ji, Y., & Müller, P. (2014). Detecting differential patterns of interaction in molecular pathways. Biostatistics, 16(2), 240-251.
[96] Yang, J., & Peng, J. (2020). Estimating time‐varying graphical models. Journal of Computational and Graphical Statistics, 29(1), 191-202. · Zbl 07499282
[97] Yu, M., Gupta, V., & Kolar, M. (2016). Statistical inference for pairwise graphical models using score matching. In D. D.Lee (ed.), M.Sugiyama (ed.), U.vonLuxburg (ed.), & R.Garnett (ed.) (Eds.), Advances in neural information processing systems 29. Curran Associates, Inc.
[98] Yu, M., Gupta, V., & Kolar, M. (2020). Simultaneous inference for pairwise graphical models with generalized score matching. Journal of Machine Learning Research, 21(91), 1-51. · Zbl 1502.62073
[99] Yuan, H., Xi, R., Chen, C., & Deng, M. (2017). Differential network analysis via lasso penalized d‐trace loss. Biometrika, 104(4), 755-770. · Zbl 07072326
[100] Yuan, M., & Lin, Y. (2007). Model selection and estimation in the Gaussian graphical model. Biometrika, 94(1), 19-35. · Zbl 1142.62408
[101] Zhao, B., Wang, Y. S., & Kolar, M. (2019). Direct estimation of differential functional graphical models. In M. I.Jordan (ed.), Y.LeCun (ed.), & S. A.Solla (ed.) (Eds.), Advances in neural information processing systems (pp. 2575-2585). Curran Associates, Inc.
[102] Zhao, S. D., Cai, T. T., & Li, H. (2014). Direct estimation of differential networks. Biometrika, 101(2), 253-268. · Zbl 1452.62865
[103] Zhou, S., Lafferty, J., & Wasserman, L. (2010). Time varying undirected graphs. Machine Learning, 80(2), 295-319. · Zbl 1475.62174
[104] Zhu, Y., & Koyejo, O. (2018). Clustered fused graphical lasso (pp. 487-496). UAI.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.