{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T17:26:44Z","timestamp":1772040404801,"version":"3.50.1"},"publisher-location":"Cham","reference-count":65,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031434204","type":"print"},{"value":"9783031434211","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-43421-1_21","type":"book-chapter","created":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T20:37:24Z","timestamp":1694983044000},"page":"349-366","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Learning Graphical Factor Models with\u00a0Riemannian Optimization"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7740-5415","authenticated-orcid":false,"given":"Alexandre","family":"Hippert-Ferrer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3003-7317","authenticated-orcid":false,"given":"Florent","family":"Bouchard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1796-8707","authenticated-orcid":false,"given":"Ammar","family":"Mian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8115-572X","authenticated-orcid":false,"given":"Titouan","family":"Vayer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3802-9015","authenticated-orcid":false,"given":"Arnaud","family":"Breloy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,18]]},"reference":[{"key":"21_CR1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"PA Absil","year":"2008","unstructured":"Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2008)"},{"key":"21_CR2","doi-asserted-by":"crossref","unstructured":"Anderson, T.W., Fang, K.T.: Theory and applications of elliptically contoured and related distributions (1990)","DOI":"10.21236\/ADA230672"},{"key":"21_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2019.107417","volume":"169","author":"A Benfenati","year":"2020","unstructured":"Benfenati, A., Chouzenoux, E., Pesquet, J.C.: Proximal approaches for matrix optimization problems: application to robust precision matrix estimation. Signal Process. 169, 107417 (2020)","journal-title":"Signal Process."},{"key":"21_CR4","doi-asserted-by":"publisher","DOI":"10.1515\/9781400827787","volume-title":"Positive Definite Matrices","author":"R Bhatia","year":"2009","unstructured":"Bhatia, R.: Positive Definite Matrices. Princeton University Press, Princeton (2009)"},{"issue":"3","key":"21_CR5","doi-asserted-by":"publisher","first-page":"1055","DOI":"10.1137\/080731347","volume":"31","author":"S Bonnabel","year":"2009","unstructured":"Bonnabel, S., Sepulchre, R.: Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank. SIAM J. Matrix Anal. Appl. 31(3), 1055\u20131070 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"21_CR6","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.1109\/TSP.2021.3054237","volume":"69","author":"F Bouchard","year":"2021","unstructured":"Bouchard, F., Breloy, A., Ginolhac, G., Renaux, A., Pascal, F.: A Riemannian framework for low-rank structured elliptical models. IEEE Trans. Signal Process. 69, 1185\u20131199 (2021)","journal-title":"IEEE Trans. Signal Process."},{"key":"21_CR7","unstructured":"Boumal, N.: An introduction to optimization on smooth manifolds. Available online, May 3 (2020)"},{"key":"21_CR8","unstructured":"Chandra, N.K., Mueller, P., Sarkar, A.: Bayesian scalable precision factor analysis for massive sparse Gaussian graphical models. arXiv preprint arXiv:2107.11316 (2021)"},{"key":"21_CR9","unstructured":"Chung, F.R.: Spectral Graph Theory, vol. 92. American Mathematical Soc. (1997)"},{"key":"21_CR10","doi-asserted-by":"crossref","unstructured":"Cordasco, G., Gargano, L.: Community detection via semi-synchronous label propagation algorithms. In: 2010 IEEE International Workshop on: Business Applications of Social Network Analysis (BASNA), pp. 1\u20138 (2010)","DOI":"10.1109\/BASNA.2010.5730298"},{"key":"21_CR11","doi-asserted-by":"publisher","first-page":"157","DOI":"10.2307\/2528966","volume":"28","author":"AP Dempster","year":"1972","unstructured":"Dempster, A.P.: Covariance selection. Biometrics 28, 157\u2013175 (1972)","journal-title":"Biometrics"},{"issue":"16","key":"21_CR12","doi-asserted-by":"publisher","first-page":"4253","DOI":"10.1109\/TSP.2018.2841892","volume":"66","author":"G Dra\u0161kovi\u0107","year":"2018","unstructured":"Dra\u0161kovi\u0107, G., Pascal, F.: New insights into the statistical properties of $${M}$$-estimators. IEEE Trans. Signal Process. 66(16), 4253\u20134263 (2018)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"21_CR13","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479895290954","volume":"20","author":"A Edelman","year":"1998","unstructured":"Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20(2), 303\u2013353 (1998)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"6","key":"21_CR14","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1109\/JSTSP.2017.2726975","volume":"11","author":"HE Egilmez","year":"2017","unstructured":"Egilmez, H.E., Pavez, E., Ortega, A.: Graph learning from data under Laplacian and structural constraints. IEEE J. Sel. Topics Sig. Process. 11(6), 825\u2013841 (2017)","journal-title":"IEEE J. Sel. Topics Sig. Process."},{"key":"21_CR15","doi-asserted-by":"publisher","first-page":"1152","DOI":"10.1214\/16-AOS1478","volume":"45","author":"S Fallat","year":"2017","unstructured":"Fallat, S., Lauritzen, S., Sadeghi, K., Uhler, C., Wermuth, N., Zwiernik, P.: Total positivity in Markov structures. Ann. Stat. 45, 1152\u20131184 (2017)","journal-title":"Ann. Stat."},{"key":"21_CR16","first-page":"1","volume":"20","author":"S Fattahi","year":"2019","unstructured":"Fattahi, S., Sojoudi, S.: Graphical lasso and thresholding: equivalence and closed-form solutions. J. Mach. Learn. Res. 20, 1\u201344 (2019)","journal-title":"J. Mach. Learn. Res."},{"key":"21_CR17","unstructured":"Finegold, M.A., Drton, M.: Robust graphical modeling with $$t$$-distributions. arXiv preprint arXiv:1408.2033 (2014)"},{"issue":"3","key":"21_CR18","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1093\/biostatistics\/kxm045","volume":"9","author":"J Friedman","year":"2008","unstructured":"Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432\u2013441 (2008)","journal-title":"Biostatistics"},{"issue":"16","key":"21_CR19","first-page":"99","volume":"17","author":"O Hein\u00e4vaara","year":"2016","unstructured":"Hein\u00e4vaara, O., Lepp\u00e4-Aho, J., Corander, J., Honkela, A.: On the inconsistency of $$\\ell _1$$-penalised sparse precision matrix estimation. BMC Bioinform. 17(16), 99\u2013107 (2016)","journal-title":"BMC Bioinform."},{"issue":"6","key":"21_CR20","doi-asserted-by":"publisher","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"MR Hestenes","year":"1952","unstructured":"Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear equation. J. Res. Natl. Bur. Stand. 49(6), 409 (1952)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"21_CR21","first-page":"379","volume":"39","author":"B Jeuris","year":"2012","unstructured":"Jeuris, B., Vandebril, R., Vandereycken, B.: A survey and comparison of contemporary algorithms for computing the matrix geometric mean. Electron. Trans. Numer. Anal. 39, 379\u2013402 (2012)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"21_CR22","unstructured":"Kai-Tai, F., Yao-Ting, Z.: Generalized Multivariate Analysis, vol. 19. Science Press Beijing and Springer-Verlag, Berlin (1990)"},{"key":"21_CR23","unstructured":"Kalofolias, V.: How to learn a graph from smooth signals. In: Artificial Intelligence and Statistics, pp. 920\u2013929. PMLR (2016)"},{"issue":"1","key":"21_CR24","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s10107-019-01370-7","volume":"176","author":"K Khamaru","year":"2019","unstructured":"Khamaru, K., Mazumder, R.: Computation of the maximum likelihood estimator in low-rank factor analysis. Math. Program. 176(1), 279\u2013310 (2019)","journal-title":"Math. Program."},{"key":"21_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1007\/978-3-319-46454-1_41","volume-title":"Computer Vision \u2013 ECCV 2016","author":"A Kovnatsky","year":"2016","unstructured":"Kovnatsky, A., Glashoff, K., Bronstein, M.M.: MADMM: a generic algorithm for non-smooth optimization on manifolds. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9909, pp. 680\u2013696. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-46454-1_41"},{"issue":"22","key":"21_CR26","first-page":"1","volume":"21","author":"S Kumar","year":"2020","unstructured":"Kumar, S., Ying, J., de Miranda Cardoso, J.V., Palomar, D.P.: A unified framework for structured graph learning via spectral constraints. J. Mach. Learn. Res. 21(22), 1\u201360 (2020)","journal-title":"J. Mach. Learn. Res."},{"key":"21_CR27","unstructured":"Lake, B., Tenenbaum, J.: Discovering structure by learning sparse graphs (2010)"},{"issue":"6B","key":"21_CR28","doi-asserted-by":"publisher","first-page":"4254","DOI":"10.1214\/09-AOS720","volume":"37","author":"C Lam","year":"2009","unstructured":"Lam, C., Fan, J.: Sparsistency and rates of convergence in large covariance matrix estimation. Ann. Stat. 37(6B), 4254\u20134278 (2009)","journal-title":"Ann. Stat."},{"issue":"4","key":"21_CR29","doi-asserted-by":"publisher","first-page":"1835","DOI":"10.1214\/17-AOS1668","volume":"47","author":"S Lauritzen","year":"2019","unstructured":"Lauritzen, S., Uhler, C., Zwiernik, P.: Maximum likelihood estimation in Gaussian models under total positivity. Ann. Stat. 47(4), 1835\u20131863 (2019)","journal-title":"Ann. Stat."},{"key":"21_CR30","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522195.001.0001","volume-title":"Graphical Models","author":"SL Lauritzen","year":"1996","unstructured":"Lauritzen, S.L.: Graphical Models, vol. 17. Clarendon Press, Oxford (1996)"},{"issue":"2","key":"21_CR31","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/S0047-259X(03)00096-4","volume":"88","author":"O Ledoit","year":"2004","unstructured":"Ledoit, O., Wolf, M.: A well-conditioned estimator for large-dimensional covariance matrices. J. Multivar. Anal. 88(2), 365\u2013411 (2004)","journal-title":"J. Multivar. Anal."},{"issue":"2","key":"21_CR32","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1093\/biostatistics\/kxj008","volume":"7","author":"H Li","year":"2006","unstructured":"Li, H., Gui, J.: Gradient directed regularization for sparse Gaussian concentration graphs, with applications to inference of genetic networks. Biostatistics 7(2), 302\u2013317 (2006)","journal-title":"Biostatistics"},{"key":"21_CR33","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1214\/aos\/1176343347","volume":"4","author":"RA Maronna","year":"1976","unstructured":"Maronna, R.A.: Robust $${M}$$-estimators of multivariate location and scatter. Ann. Stat. 4, 51\u201367 (1976)","journal-title":"Ann. Stat."},{"key":"21_CR34","series-title":"Signals and Communication Technology","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/978-3-030-65459-7_10","volume-title":"Progress in Information Geometry","author":"G Marti","year":"2021","unstructured":"Marti, G., Nielsen, F., Bi\u0144kowski, M., Donnat, P.: A review of two decades of correlations, hierarchies, networks and clustering in financial markets. In: Nielsen, F. (ed.) Progress in Information Geometry. SCT, pp. 245\u2013274. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-65459-7_10"},{"key":"21_CR35","unstructured":"Massart, E., Absil, P.A.: Quotient geometry with simple geodesics for the manifold of fixed-rank positive-semidefinite matrices. Technical Report UCL-INMA-2018.06 (2018)"},{"key":"21_CR36","doi-asserted-by":"publisher","first-page":"2125","DOI":"10.1214\/12-EJS740","volume":"6","author":"R Mazumder","year":"2012","unstructured":"Mazumder, R., Hastie, T.: The graphical lasso: new insights and alternatives. Electron. J. Stat. 6, 2125 (2012)","journal-title":"Electron. J. Stat."},{"key":"21_CR37","unstructured":"Meng, Z., Eriksson, B., Hero, A.: Learning latent variable Gaussian graphical models. In: International Conference on Machine Learning, pp. 1269\u20131277. PMLR (2014)"},{"key":"21_CR38","first-page":"593","volume":"12","author":"G Meyer","year":"2011","unstructured":"Meyer, G., Bonnabel, S., Sepulchre, R.: Regression on fixed-rank positive semidefinite matrices: a Riemannian approach. J. Mach. Learn. Res. 12, 593\u2013625 (2011)","journal-title":"J. Mach. Learn. Res."},{"key":"21_CR39","first-page":"19989","volume":"34","author":"JV de Miranda Cardoso","year":"2021","unstructured":"de Miranda Cardoso, J.V., Ying, J., Palomar, D.: Graphical models in heavy-tailed markets. Adv. Neural. Inf. Process. Syst. 34, 19989\u201320001 (2021)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"21_CR40","unstructured":"Neuman, A.M., Xie, Y., Sun, Q.: Restricted Riemannian geometry for positive semidefinite matrices. arXiv preprint arXiv:2105.14691 (2021)"},{"issue":"23","key":"21_CR41","doi-asserted-by":"publisher","first-page":"8577","DOI":"10.1073\/pnas.0601602103","volume":"103","author":"MEJ Newman","year":"2006","unstructured":"Newman, M.E.J.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577\u20138582 (2006)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"21_CR42","doi-asserted-by":"crossref","unstructured":"Osherson, D.N., Stern, J., Wilkie, O., Stob, M., Smith, E.E.: Default probability. Cogn. Sci. 15(2), 251\u2013269 (1991)","DOI":"10.1207\/s15516709cog1502_3"},{"key":"21_CR43","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.jvolgeores.2017.03.027","volume":"344","author":"A Peltier","year":"2017","unstructured":"Peltier, A., Froger, J.L., Villeneuve, N., Catry, T.: Assessing the reliability and consistency of InSAR and GNSS data for retrieving 3D-displacement rapid changes, the example of the 2015 Piton de la Fournaise eruptions. J. Volcanol. Geoth. Res. 344, 106\u2013120 (2017)","journal-title":"J. Volcanol. Geoth. Res."},{"issue":"4","key":"21_CR44","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1016\/j.jmva.2006.11.012","volume":"98","author":"D Robertson","year":"2007","unstructured":"Robertson, D., Symons, J.: Maximum likelihood factor analysis with rank-deficient sample covariance matrices. J. Multivar. Anal. 98(4), 813\u2013828 (2007)","journal-title":"J. Multivar. Anal."},{"issue":"1","key":"21_CR45","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF02293851","volume":"47","author":"DB Rubin","year":"1982","unstructured":"Rubin, D.B., Thayer, D.T.: EM algorithms for ML factor analysis. Psychometrika 47(1), 69\u201376 (1982)","journal-title":"Psychometrika"},{"issue":"497","key":"21_CR46","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1080\/01621459.2011.645783","volume":"107","author":"X Shen","year":"2012","unstructured":"Shen, X., Pan, W., Zhu, Y.: Likelihood-based selection and sharp parameter estimation. J. Am. Stat. Assoc. 107(497), 223\u2013232 (2012)","journal-title":"J. Am. Stat. Assoc."},{"issue":"3","key":"21_CR47","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1109\/MSP.2012.2235192","volume":"30","author":"DI Shuman","year":"2013","unstructured":"Shuman, D.I., Narang, S.K., Frossard, P., Ortega, A., Vandergheynst, P.: The emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Process. Mag. 30(3), 83\u201398 (2013)","journal-title":"IEEE Signal Process. Mag."},{"key":"21_CR48","first-page":"211","volume":"11","author":"LT Skovgaard","year":"1984","unstructured":"Skovgaard, L.T.: A Riemannian geometry of the multivariate normal model. Scand. J. Stat. 11, 211\u2013223 (1984)","journal-title":"Scand. J. Stat."},{"issue":"2","key":"21_CR49","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1016\/j.neuroimage.2010.08.063","volume":"54","author":"SM Smith","year":"2011","unstructured":"Smith, S.M., et al.: Network modelling methods for FMRI. Neuroimage 54(2), 875\u2013891 (2011)","journal-title":"Neuroimage"},{"issue":"5","key":"21_CR50","doi-asserted-by":"publisher","first-page":"1610","DOI":"10.1109\/TSP.2005.845428","volume":"53","author":"ST Smith","year":"2005","unstructured":"Smith, S.T.: Covariance, subspace, and intrinsic Cram\u00e8r-Rao bounds. IEEE Trans. Signal Process. 53(5), 1610\u20131630 (2005)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"21_CR51","doi-asserted-by":"publisher","first-page":"1361","DOI":"10.1029\/2018JB016856","volume":"124","author":"D Smittarello","year":"2019","unstructured":"Smittarello, D., Cayol, V., Pinel, V., Peltier, A., Froger, J.L., Ferrazzini, V.: Magma propagation at Piton de la Fournaise from joint inversion of InSAR and GNSS. J. Geophys. Res. Solid Earth 124(2), 1361\u20131387 (2019)","journal-title":"J. Geophys. Res. Solid Earth"},{"issue":"3","key":"21_CR52","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1038\/nrg3833","volume":"16","author":"O Stegle","year":"2015","unstructured":"Stegle, O., Teichmann, S.A., Marioni, J.C.: Computational and analytical challenges in single-cell transcriptomics. Nat. Rev. Genet. 16(3), 133\u2013145 (2015)","journal-title":"Nat. Rev. Genet."},{"issue":"1","key":"21_CR53","first-page":"1","volume":"18","author":"DA Tarzanagh","year":"2018","unstructured":"Tarzanagh, D.A., Michailidis, G.: Estimation of graphical models through structured norm minimization. J. Mach. Learn. Res. 18(1), 1\u201348 (2018)","journal-title":"J. Mach. Learn. Res."},{"issue":"3","key":"21_CR54","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1111\/1467-9868.00196","volume":"61","author":"ME Tipping","year":"1999","unstructured":"Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. J. Roy. Stat. Soc. Ser. B (Stat. Methodol.) 61(3), 611\u2013622 (1999)","journal-title":"J. Roy. Stat. Soc. Ser. B (Stat. Methodol.)"},{"key":"21_CR55","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1214\/aos\/1176350263","volume":"15","author":"DE Tyler","year":"1987","unstructured":"Tyler, D.E.: A distribution-free $${M}$$-estimator of multivariate scatter. Ann. Stat. 15, 234\u2013251 (1987)","journal-title":"Ann. Stat."},{"issue":"2","key":"21_CR56","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1093\/imanum\/drs006","volume":"33","author":"B Vandereycken","year":"2012","unstructured":"Vandereycken, B., Absil, P.A., Vandewalle, S.: A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank. IMA J. Numer. Anal. 33(2), 481\u2013514 (2012)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"21_CR57","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1007\/s10959-010-0338-z","volume":"25","author":"R Vershynin","year":"2012","unstructured":"Vershynin, R.: How close is the sample covariance matrix to the actual covariance matrix? J. Theor. Probab. 25(3), 655\u2013686 (2012)","journal-title":"J. Theor. Probab."},{"issue":"4","key":"21_CR58","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1093\/biomet\/asr037","volume":"98","author":"D Vogel","year":"2011","unstructured":"Vogel, D., Fried, R.: Elliptical graphical modelling. Biometrika 98(4), 935\u2013951 (2011)","journal-title":"Biometrika"},{"key":"21_CR59","unstructured":"Wald, Y., Noy, N., Elidan, G., Wiesel, A.: Globally optimal learning for structured elliptical losses. In: Advances in Neural Information Processing Systems, vol. 32 (2019)"},{"key":"21_CR60","first-page":"7101","volume":"33","author":"J Ying","year":"2020","unstructured":"Ying, J., de Miranda Cardoso, J.V., Palomar, D.: Nonconvex sparse graph learning under Laplacian constrained graphical model. Adv. Neural. Inf. Process. Syst. 33, 7101\u20137113 (2020)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"21_CR61","first-page":"1771","volume":"11","author":"R Yoshida","year":"2010","unstructured":"Yoshida, R., West, M.: Bayesian learning in sparse graphical factor models via variational mean-field annealing. J. Mach. Learn. Res. 11, 1771\u20131798 (2010)","journal-title":"J. Mach. Learn. Res."},{"issue":"16","key":"21_CR62","doi-asserted-by":"publisher","first-page":"4141","DOI":"10.1109\/TSP.2013.2267740","volume":"61","author":"T Zhang","year":"2013","unstructured":"Zhang, T., Wiesel, A., Greco, M.S.: Multivariate generalized Gaussian distribution: convexity and graphical models. IEEE Trans. Signal Process. 61(16), 4141\u20134148 (2013)","journal-title":"IEEE Trans. Signal Process."},{"issue":"16\u201318","key":"21_CR63","doi-asserted-by":"publisher","first-page":"2217","DOI":"10.1016\/j.neucom.2005.07.011","volume":"69","author":"J Zhao","year":"2006","unstructured":"Zhao, J., Jiang, Q.: Probabilistic PCA for $$t$$-distributions. Neurocomputing 69(16\u201318), 2217\u20132226 (2006)","journal-title":"Neurocomputing"},{"issue":"16","key":"21_CR64","doi-asserted-by":"publisher","first-page":"4231","DOI":"10.1109\/TSP.2019.2925602","volume":"67","author":"L Zhao","year":"2019","unstructured":"Zhao, L., Wang, Y., Kumar, S., Palomar, D.P.: Optimization algorithms for graph Laplacian estimation via ADMM and MM. IEEE Trans. Signal Process. 67(16), 4231\u20134244 (2019)","journal-title":"IEEE Trans. Signal Process."},{"key":"21_CR65","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-45096-0_1","volume-title":"Computer Aided Systems Theory \u2013 EUROCAST 2019","author":"R Zhou","year":"2020","unstructured":"Zhou, R., Liu, J., Kumar, S., Palomar, D.P.: Robust factor analysis parameter estimation. In: Moreno-D\u00edaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2019. LNCS, vol. 12014, pp. 3\u201311. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45096-0_1"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases: Research Track"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-43421-1_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T23:09:58Z","timestamp":1703200198000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-43421-1_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031434204","9783031434211"],"references-count":65,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-43421-1_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"18 September 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Turin","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 September 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 September 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/2023.ecmlpkdd.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"CMT","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"829","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"196","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"24% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.63","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4.5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Applied Data Science Track: 239 submissions, 58 accepted papers; Demo Track: 31 submissions, 16 accepted papers.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}