{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T20:05:53Z","timestamp":1776456353332,"version":"3.51.2"},"reference-count":84,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T00:00:00Z","timestamp":1702857600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T00:00:00Z","timestamp":1702857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s10994-023-06410-0","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T16:47:46Z","timestamp":1702918066000},"page":"891-932","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Heterogeneous multi-task feature learning with mixed $$\\ell _{2,1}$$ regularization"],"prefix":"10.1007","volume":"113","author":[{"given":"Yuan","family":"Zhong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8057-5100","authenticated-orcid":false,"given":"Xin","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,18]]},"reference":[{"issue":"2","key":"6410_CR1","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1214\/12-AOS1000","volume":"40","author":"A Agarwal","year":"2012","unstructured":"Agarwal, A., Negahban, S., & Wainwright, M. J. (2012). Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions. The Annals of Statistics, 40(2), 1171\u20131197.","journal-title":"The Annals of Statistics"},{"issue":"61","key":"6410_CR2","first-page":"1817","volume":"6","author":"RK Ando","year":"2005","unstructured":"Ando, R. K., & Zhang, T. (2005). A framework for learning predictive structures from multiple tasks and unlabeled data. Journal of Machine Learning Research, 6(61), 1817\u20131853.","journal-title":"Journal of Machine Learning Research"},{"key":"6410_CR3","doi-asserted-by":"crossref","unstructured":"Argyriou, A., Evgeniou, T., & Pontil, M. (2006). Multi-task feature learning. In: Proceedings of the 19th international conference on neural information processing systems. MIT Press, Cambridge, MA, USA, NIPS\u201906, pp. 41\u201348.","DOI":"10.7551\/mitpress\/7503.003.0010"},{"issue":"40","key":"6410_CR4","first-page":"1179","volume":"9","author":"FR Bach","year":"2008","unstructured":"Bach, F. R. (2008). Consistency of the group lasso and multiple kernel learning. Journal of Machine Learning Research, 9(40), 1179\u20131225.","journal-title":"Journal of Machine Learning Research"},{"issue":"3","key":"6410_CR5","doi-asserted-by":"publisher","first-page":"203","DOI":"10.3390\/stats3030016","volume":"3","author":"H Bai","year":"2020","unstructured":"Bai, H., Zhong, Y., Gao, X., et al. (2020). Multivariate mixed response model with pairwise composite-likelihood method. Stats, 3(3), 203\u2013220.","journal-title":"Stats"},{"issue":"1","key":"6410_CR6","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., & Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1), 183\u2013202.","journal-title":"SIAM Journal on Imaging Sciences"},{"issue":"4","key":"6410_CR7","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1214\/08-AOS620","volume":"37","author":"PJ Bickel","year":"2009","unstructured":"Bickel, P. J., Ritov, Y., & Tsybakov, A. B. (2009). Simultaneous analysis of Lasso and dantzig selector. The Annals of Statistics, 37(4), 1705\u20131732.","journal-title":"The Annals of Statistics"},{"issue":"20","key":"6410_CR8","doi-asserted-by":"publisher","first-page":"3282","DOI":"10.4161\/15384101.2014.954454","volume":"13","author":"C Cadenas","year":"2014","unstructured":"Cadenas, C., van de Sandt, L., Edlund, K., et al. (2014). Loss of circadian clock gene expression is associated with tumor progression in breast cancer. Cell Cycle, 13(20), 3282\u20133291. PMID: 25485508.","journal-title":"Cell Cycle"},{"key":"6410_CR9","unstructured":"Cao, H., & Schwarz, E. (2022). RMTL: Regularized multi-task learning. https:\/\/CRAN.R-project.org\/package=RMTL, r package version 0.9.9."},{"issue":"1","key":"6410_CR10","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1023\/A:1007379606734","volume":"28","author":"R Caruana","year":"1997","unstructured":"Caruana, R. (1997). Multitask learning. Machine Learning, 28(1), 41\u201375.","journal-title":"Machine Learning"},{"issue":"3","key":"6410_CR11","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1093\/biomet\/91.3.729","volume":"91","author":"DR Cox","year":"2004","unstructured":"Cox, D. R., & Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities. Biometrika, 91(3), 729\u2013737.","journal-title":"Biometrika"},{"key":"6410_CR12","unstructured":"U.S. Department of Health and Human Services. (2010). Community Health Status Indicators (CHSI) to Combat Obesity, Heart Disease and Cancer 1996\u20132003 (p. 2010). Washington, D.C., USA: US Department of Health and Human Services."},{"key":"6410_CR13","unstructured":"Ekvall, K.O., & Molstad, A.J. (2021). mmrr: Mixed-type multivariate response regression. R package version 0.1."},{"key":"6410_CR14","doi-asserted-by":"publisher","unstructured":"Ekvall, K. O., & Molstad, A. J. (2022). Mixed-type multivariate response regression with covariance estimation. Statistics in Medicine,41(15), 2768\u20132785. https:\/\/doi.org\/10.1002\/sim.9383, onlinelibrary.wiley.com\/doi\/abs\/10.1002\/sim.9383.","DOI":"10.1002\/sim.9383"},{"issue":"6","key":"6410_CR15","doi-asserted-by":"publisher","first-page":"3042","DOI":"10.1109\/TSP.2010.2044837","volume":"58","author":"YC Eldar","year":"2010","unstructured":"Eldar, Y. C., Kuppinger, P., & Bolcskei, H. (2010). Block-sparse signals: Uncertainty relations and efficient recovery. IEEE Transactions on Signal Processing, 58(6), 3042\u20133054.","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"5","key":"6410_CR16","doi-asserted-by":"publisher","first-page":"2622","DOI":"10.1214\/19-AOS1900","volume":"48","author":"EX Fang","year":"2020","unstructured":"Fang, E. X., Ning, Y., & Li, R. (2020). Test of significance for high-dimensional longitudinal data. The Annals of Statistics, 48(5), 2622\u20132645.","journal-title":"The Annals of Statistics"},{"issue":"2","key":"6410_CR17","doi-asserted-by":"publisher","first-page":"814","DOI":"10.1214\/17-AOS1568","volume":"46","author":"J Fan","year":"2018","unstructured":"Fan, J., Liu, H., Sun, Q., et al. (2018). I-lamm for sparse learning: Simultaneous control of algorithmic complexity and statistical error. The Annals of Statistics, 46(2), 814\u2013841.","journal-title":"The Annals of Statistics"},{"issue":"3","key":"6410_CR18","doi-asserted-by":"publisher","first-page":"1239","DOI":"10.1214\/20-aos1980","volume":"49","author":"J Fan","year":"2021","unstructured":"Fan, J., Wang, W., & Zhu, Z. (2021). A shrinkage principle for heavy-tailed data: High-dimensional robust low-rank matrix recovery. Annals of statistics, 49(3), 1239\u20131266. https:\/\/doi.org\/10.1214\/20-aos1980","journal-title":"Annals of statistics"},{"key":"6410_CR19","unstructured":"Gao, X., Zhong, Y., & Carroll, R. J. (2022). FusionLearn: Fusion Learning. https:\/\/CRAN.R-project.org\/package=FusionLearn, r package version 0.2.1."},{"issue":"2","key":"6410_CR20","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1093\/biomet\/asx023","volume":"104","author":"X Gao","year":"2017","unstructured":"Gao, X., & Carroll, R. J. (2017). Data integration with high dimensionality. Biometrika, 104(2), 251\u2013272.","journal-title":"Biometrika"},{"issue":"492","key":"6410_CR21","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1198\/jasa.2010.tm09414","volume":"105","author":"X Gao","year":"2010","unstructured":"Gao, X., & Song, P. X. K. (2010). Composite likelihood Bayesian information criteria for model selection in high-dimensional data. Journal of the American Statistical Association, 105(492), 1531\u20131540.","journal-title":"Journal of the American Statistical Association"},{"issue":"21","key":"6410_CR22","doi-asserted-by":"publisher","first-page":"4465","DOI":"10.1093\/bioinformatics\/btz223","volume":"35","author":"X Gao","year":"2019","unstructured":"Gao, X., & Zhong, Y. (2019). Fusionlearn: a biomarker selection algorithm on cross-platform data. Bioinformatics, 35(21), 4465\u20134468.","journal-title":"Bioinformatics"},{"issue":"14","key":"6410_CR23","doi-asserted-by":"publisher","first-page":"6892","DOI":"10.1093\/nar\/gkt469","volume":"41","author":"L Gaughan","year":"2013","unstructured":"Gaughan, L., Stockley, J., Coffey, K., et al. (2013). KDM4B is a master regulator of the estrogen receptor signalling cascade. Nucleic Acids Research, 41(14), 6892\u20136904. https:\/\/doi.org\/10.1093\/nar\/gkt469","journal-title":"Nucleic Acids Research"},{"issue":"4","key":"6410_CR24","doi-asserted-by":"publisher","first-page":"1208","DOI":"10.1214\/aoms\/1177705693","volume":"31","author":"VP Godambe","year":"1960","unstructured":"Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation. The Annals of Mathematical Statistics, 31(4), 1208\u20131211.","journal-title":"The Annals of Mathematical Statistics"},{"issue":"2","key":"6410_CR25","doi-asserted-by":"publisher","first-page":"I1","DOI":"10.1186\/1752-0509-8-S2-I1","volume":"8","author":"D Gomez-Cabrero","year":"2014","unstructured":"Gomez-Cabrero, D., Abugessaisa, I., Maier, D., et al. (2014). Data integration in the era of omics: Current and future challenges. BMC Systems Biology, 8(2), I1.","journal-title":"BMC Systems Biology"},{"issue":"55","key":"6410_CR26","first-page":"2979","volume":"14","author":"P Gong","year":"2013","unstructured":"Gong, P., Ye, J., & Zhang, C. (2013). Multi-stage multi-task feature learning. Journal of Machine Learning Research, 14(55), 2979\u20133010.","journal-title":"Journal of Machine Learning Research"},{"issue":"18","key":"6410_CR27","doi-asserted-by":"publisher","first-page":"1873","DOI":"10.1001\/jama.2011.593","volume":"305","author":"C Hatzis","year":"2011","unstructured":"Hatzis, C., Pusztai, L., Valero, V., et al. (2011). A genomic predictor of response and survival following taxane-anthracycline chemotherapy for invasive breast cancer. JAMA, 305(18), 1873\u20131881.","journal-title":"JAMA"},{"issue":"none","key":"6410_CR28","doi-asserted-by":"publisher","first-page":"1184","DOI":"10.1214\/11-EJS638","volume":"5","author":"M Hebiri","year":"2011","unstructured":"Hebiri, M., & van de Geer, S. (2011). The Smooth-Lasso and other $$\\ell _1+\\ell _2$$-penalized methods. Electronic Journal of Statistics, 5(none), 1184\u20131226.","journal-title":"Electronic Journal of Statistics"},{"key":"6410_CR29","doi-asserted-by":"crossref","unstructured":"Heimes, A. S., H\u00e4rtner, F., Almstedt, K., et al. (2020). Prognostic significance of interferon-$$\\gamma$$ and its signaling pathway in early breast cancer depends on the molecular subtypes. International Journal of Molecular Sciences,21(19).","DOI":"10.3390\/ijms21197178"},{"issue":"1","key":"6410_CR30","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1186\/1471-2105-11-276","volume":"11","author":"B Hellwig","year":"2010","unstructured":"Hellwig, B., Hengstler, J. G., Schmidt, M., et al. (2010). Comparison of scores for bimodality of gene expression distributions and genome-wide evaluation of the prognostic relevance of high-scoring genes. BMC Bioinformatics, 11(1), 276.","journal-title":"BMC Bioinformatics"},{"issue":"2","key":"6410_CR31","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s10549-013-2763-z","volume":"143","author":"M Itoh","year":"2014","unstructured":"Itoh, M., Iwamoto, T., Matsuoka, J., et al. (2014). Estrogen receptor (er) mrna expression and molecular subtype distribution in er-negative\/progesterone receptor-positive breast cancers. Breast Cancer Research and Treatment, 143(2), 403\u2013409.","journal-title":"Breast Cancer Research and Treatment"},{"issue":"21","key":"6410_CR32","doi-asserted-by":"publisher","first-page":"10292","DOI":"10.1158\/0008-5472.CAN-05-4414","volume":"66","author":"AV Ivshina","year":"2006","unstructured":"Ivshina, A. V., George, J., Senko, O., et al. (2006). Genetic reclassification of histologic grade delineates new clinical subtypes of breast cancer. Cancer Research, 66(21), 10292\u201310301.","journal-title":"Cancer Research"},{"key":"6410_CR33","volume-title":"Advances in neural information processing systems","author":"A Jalali","year":"2010","unstructured":"Jalali, A., Sanghavi, S., Ruan, C., et al. (2010). A dirty model for multi-task learning. In J. Lafferty, C. Williams, J. Shawe-Taylor, et al. (Eds.), Advances in neural information processing systems.  (Vol. 23). Curran Associates Inc."},{"issue":"1","key":"6410_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12885-018-5221-9","volume":"19","author":"N Kanomata","year":"2019","unstructured":"Kanomata, N., Kurebayashi, J., Koike, Y., et al. (2019). Cd1d-and pja2-related immune microenvironment differs between invasive breast carcinomas with and without a micropapillary feature. BMC Cancer, 19(1), 1\u20139.","journal-title":"BMC Cancer"},{"key":"6410_CR35","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1016\/j.gdata.2014.09.014","volume":"2","author":"T Karn","year":"2014","unstructured":"Karn, T., Rody, A., M\u00fcller, V., et al. (2014). Control of dataset bias in combined affymetrix cohorts of triple negative breast cancer. Genomics Data, 2, 354\u2013356.","journal-title":"Genomics Data"},{"key":"6410_CR36","first-page":"220","volume":"80","author":"B Lindsay","year":"1988","unstructured":"Lindsay, B. (1988). Composite likelihood methods. Contemporary Mathematics, 80, 220\u2013239.","journal-title":"Contemporary Mathematics"},{"key":"6410_CR37","unstructured":"Liu, J,. Ji, S., & Ye, J. (2009). Multi-task feature learning via efficient $$l_{2,1}$$-norm minimization. In: Proceedings of the twenty-fifth conference on uncertainty in artificial intelligence. AUAI Press, Arlington, Virginia, USA, UAI \u201909, p 339-348."},{"issue":"1","key":"6410_CR38","doi-asserted-by":"publisher","first-page":"262","DOI":"10.21873\/invivo.13076","volume":"37","author":"CL Liu","year":"2023","unstructured":"Liu, C. L., Cheng, S. P., Huang, W. C., et al. (2023). Aberrant expression of solute carrier family 35 member a2 correlates with tumor progression in breast cancer. In Vivo, 37(1), 262\u2013269.","journal-title":"In Vivo"},{"issue":"1","key":"6410_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-11-181","volume":"11","author":"Q Liu","year":"2010","unstructured":"Liu, Q., Xu, Q., Zheng, V. W., et al. (2010). Multi-task learning for cross-platform sirna efficacy prediction: An in-silico study. BMC Bioinformatics, 11(1), 1\u201316.","journal-title":"BMC Bioinformatics"},{"issue":"1","key":"6410_CR40","doi-asserted-by":"publisher","first-page":"1993","DOI":"10.1214\/21-EJS1831","volume":"15","author":"Y Li","year":"2021","unstructured":"Li, Y., Xu, W., & Gao, X. (2021). Graphical-model based high dimensional generalized linear models. Electronic Journal of Statistics, 15(1), 1993\u20132028.","journal-title":"Electronic Journal of Statistics"},{"issue":"19","key":"6410_CR41","first-page":"559","volume":"16","author":"PL Loh","year":"2015","unstructured":"Loh, P. L., & Wainwright, M. J. (2015). Regularized m-estimators with nonconvexity: Statistical and algorithmic theory for local optima. Journal of Machine Learning Research, 16(19), 559\u2013616.","journal-title":"Journal of Machine Learning Research"},{"issue":"6","key":"6410_CR42","doi-asserted-by":"publisher","first-page":"2455","DOI":"10.1214\/16-AOS1530","volume":"45","author":"PL Loh","year":"2017","unstructured":"Loh, P. L., & Wainwright, M. J. (2017). Support recovery without incoherence: A case for nonconvex regularization. The Annals of Statistics, 45(6), 2455\u20132482.","journal-title":"The Annals of Statistics"},{"issue":"4","key":"6410_CR43","doi-asserted-by":"publisher","first-page":"2164","DOI":"10.1214\/11-AOS896","volume":"39","author":"K Lounici","year":"2011","unstructured":"Lounici, K., Pontil, M., van de Geer, S., et al. (2011). Oracle inequalities and optimal inference under group sparsity. The Annals of Statistics, 39(4), 2164\u20132204.","journal-title":"The Annals of Statistics"},{"key":"6410_CR44","volume-title":"Generalized Linear Models, Chapman and Hall\/CRC Monographs on Statistics and Applied Probability Series","author":"P McCullagh","year":"1989","unstructured":"McCullagh, P., & Nelder, J. (1989). Generalized Linear Models, Chapman and Hall\/CRC Monographs on Statistics and Applied Probability Series (2nd ed.). London: Chapman & Hall.","edition":"2"},{"issue":"1","key":"6410_CR45","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1214\/07-AOS582","volume":"37","author":"N Meinshausen","year":"2009","unstructured":"Meinshausen, N., & Yu, B. (2009). Lasso-type recovery of sparse representations for high-dimensional data. The Annals of Statistics, 37(1), 246\u2013270.","journal-title":"The Annals of Statistics"},{"issue":"4","key":"6410_CR46","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1214\/12-STS400","volume":"27","author":"SN Negahban","year":"2012","unstructured":"Negahban, S. N., Ravikumar, P., Wainwright, M. J., et al. (2012). A unified framework for high-dimensional analysis of $$m$$-estimators with decomposable regularizers. Statistical Science, 27(4), 538\u2013557.","journal-title":"Statistical Science"},{"issue":"6","key":"6410_CR47","doi-asserted-by":"publisher","first-page":"3841","DOI":"10.1109\/TIT.2011.2144150","volume":"57","author":"SN Negahban","year":"2011","unstructured":"Negahban, S. N., & Wainwright, M. J. (2011). Simultaneous support recovery in high dimensions: Benefits and perils of block $$\\ell _{1}\/\\ell _{\\infty }$$-regularization. IEEE Transactions on Information Theory, 57(6), 3841\u20133863.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"6410_CR48","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10107-012-0629-5","volume":"140","author":"Y Nesterov","year":"2013","unstructured":"Nesterov, Y. (2013). Gradient methods for minimizing composite functions. Mathematical Programming, 140(1), 125\u2013161.","journal-title":"Mathematical Programming"},{"issue":"1","key":"6410_CR49","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1214\/16-AOS1448","volume":"45","author":"Y Ning","year":"2017","unstructured":"Ning, Y., & Liu, H. (2017). A general theory of hypothesis tests and confidence regions for sparse high dimensional models. The Annals of Statistics, 45(1), 158\u2013195.","journal-title":"The Annals of Statistics"},{"issue":"2","key":"6410_CR50","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s11222-008-9111-x","volume":"20","author":"G Obozinski","year":"2010","unstructured":"Obozinski, G., Taskar, B., & Jordan, M. I. (2010). Joint covariate selection and joint subspace selection for multiple classification problems. Statistics and Computing, 20(2), 231\u2013252.","journal-title":"Statistics and Computing"},{"issue":"1","key":"6410_CR51","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/09-AOS776","volume":"39","author":"G Obozinski","year":"2011","unstructured":"Obozinski, G., Wainwright, M. J., & Jordan, M. I. (2011). Support union recovery in high-dimensional multivariate regression. The Annals of Statistics, 39(1), 1\u201347.","journal-title":"The Annals of Statistics"},{"key":"6410_CR52","doi-asserted-by":"publisher","DOI":"10.1016\/j.gene.2023.147174","volume":"857","author":"Y Ouyang","year":"2023","unstructured":"Ouyang, Y., Lu, W., Wang, Y., et al. (2023). Integrated analysis of mrna and extrachromosomal circular dna profiles to identify the potential mrna biomarkers in breast cancer. Gene, 857, 147174. https:\/\/doi.org\/10.1016\/j.gene.2023.147174","journal-title":"Gene"},{"issue":"3","key":"6410_CR53","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/BF02294364","volume":"52","author":"WY Poon","year":"1987","unstructured":"Poon, W. Y., & Lee, S. Y. (1987). Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients. Psychometrika, 52(3), 409\u2013430.","journal-title":"Psychometrika"},{"issue":"8","key":"6410_CR54","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1109\/TNN.2011.2157521","volume":"22","author":"A Rakotomamonjy","year":"2011","unstructured":"Rakotomamonjy, A., Flamary, R., Gasso, G., et al. (2011). $$\\ell _{p}-\\ell _{q}$$ penalty for sparse linear and sparse multiple kernel multitask learning. IEEE Transactions on Neural Networks, 22(8), 1307\u20131320.","journal-title":"IEEE Transactions on Neural Networks"},{"issue":"3","key":"6410_CR55","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1214\/09-AOS691","volume":"38","author":"P Ravikumar","year":"2010","unstructured":"Ravikumar, P., Wainwright, M. J., & Lafferty, J. D. (2010). High-dimensional Ising model selection using $$\\ell _1$$-regularized logistic regression. The Annals of Statistics, 38(3), 1287\u20131319. https:\/\/doi.org\/10.1214\/09-AOS691","journal-title":"The Annals of Statistics"},{"issue":"5","key":"6410_CR56","doi-asserted-by":"publisher","first-page":"R97","DOI":"10.1186\/bcr3035","volume":"13","author":"A Rody","year":"2011","unstructured":"Rody, A., Karn, T., Liedtke, C., et al. (2011). A clinically relevant gene signature in triple negative and basal-like breast cancer. Breast Cancer Research, 13(5), R97.","journal-title":"Breast Cancer Research"},{"issue":"13","key":"6410_CR57","doi-asserted-by":"publisher","first-page":"5405","DOI":"10.1158\/0008-5472.CAN-07-5206","volume":"68","author":"M Schmidt","year":"2008","unstructured":"Schmidt, M., B\u00f6hm, D., von T\u00f6rne, C., et al. (2008). The humoral immune system has a key prognostic impact in node-negative breast cancer. Cancer Research, 68(13), 5405\u20135413.","journal-title":"Cancer Research"},{"key":"6410_CR58","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13058-018-1046-3","volume":"20","author":"A Sethuraman","year":"2018","unstructured":"Sethuraman, A., Brown, M., Krutilina, R., et al. (2018). Bhlhe40 confers a pro-survival and pro-metastatic phenotype to breast cancer cells by modulating hbegf secretion. Breast Cancer Research, 20, 1\u201317.","journal-title":"Breast Cancer Research"},{"issue":"38","key":"6410_CR59","doi-asserted-by":"publisher","first-page":"61000","DOI":"10.18632\/oncotarget.11314","volume":"7","author":"D \u0160kalamera","year":"2016","unstructured":"\u0160kalamera, D., Dahmer-Heath, M., Stevenson, A. J., et al. (2016). Genome-wide gain-of-function screen for genes that induce epithelial-to-mesenchymal transition in breast cancer. Oncotarget, 7(38), 61000\u201361020. https:\/\/doi.org\/10.18632\/oncotarget.11314","journal-title":"Oncotarget"},{"issue":"529","key":"6410_CR60","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1080\/01621459.2018.1543124","volume":"115","author":"Q Sun","year":"2020","unstructured":"Sun, Q., Zhou, W. X., & Fan, J. (2020). Adaptive huber regression. Journal of the American Statistical Association, 115(529), 254\u2013265.","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"6410_CR61","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.ebiom.2015.01.008","volume":"2","author":"H Tang","year":"2015","unstructured":"Tang, H., Sebti, S., Titone, R., et al. (2015). Decreased becn1 mrna expression in human breast cancer is associated with estrogen receptor-negative subtypes and poor prognosis. EBioMedicine, 2(3), 255\u2013263.","journal-title":"EBioMedicine"},{"issue":"22","key":"6410_CR62","doi-asserted-by":"publisher","first-page":"29705","DOI":"10.1007\/s11042-018-6463-x","volume":"77","author":"KH Thung","year":"2018","unstructured":"Thung, K. H., & Wee, C. Y. (2018). A brief review on multi-task learning. Multimedia Tools and Applications, 77(22), 29705\u201329725.","journal-title":"Multimedia Tools and Applications"},{"issue":"1","key":"6410_CR63","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267\u2013288.","journal-title":"Journal of the Royal Statistical Society: Series B (Methodological)"},{"key":"6410_CR64","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.1214\/09-EJS506","volume":"3","author":"SA van de Geer","year":"2009","unstructured":"van de Geer, S. A., & B\u00fchlmann, P. (2009). On the conditions used to prove oracle results for the lasso. Electronic Journal of Statistics, 3, 1360\u20131392.","journal-title":"Electronic Journal of Statistics"},{"issue":"3","key":"6410_CR65","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1214\/14-AOS1221","volume":"42","author":"S van de Geer","year":"2014","unstructured":"van de Geer, S., B\u00fchlmann, P., Ritov, Y., et al. (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics, 42(3), 1166\u20131202.","journal-title":"The Annals of Statistics"},{"issue":"4","key":"6410_CR66","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1214\/12-STS397","volume":"27","author":"S van de Geer","year":"2012","unstructured":"van de Geer, S., & M\u00fcller, P. (2012). Quasi-likelihood and\/or robust estimation in high dimensions. Statistical Sciences, 27(4), 469\u2013480.","journal-title":"Statistical Sciences"},{"issue":"1","key":"6410_CR67","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10182-008-0060-7","volume":"92","author":"C Varin","year":"2008","unstructured":"Varin, C. (2008). On composite marginal likelihoods. AStA Advances in Statistical Analysis, 92(1), 1.","journal-title":"AStA Advances in Statistical Analysis"},{"key":"6410_CR68","doi-asserted-by":"crossref","unstructured":"Wainwright, M.J. (2019). High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press.","DOI":"10.1017\/9781108627771"},{"issue":"1","key":"6410_CR69","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1109\/TIT.2014.2375328","volume":"61","author":"W Wang","year":"2015","unstructured":"Wang, W., Liang, Y., & Xing, E. P. (2015). Collective support recovery for multi-design multi-response linear regression. IEEE Transactions on Information Theory, 61(1), 513\u2013534.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"6410_CR70","first-page":"439","volume":"61","author":"RWM Wedderburn","year":"1974","unstructured":"Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the gauss-newton method. Biometrika, 61(3), 439\u2013447.","journal-title":"Biometrika"},{"issue":"43","key":"6410_CR71","doi-asserted-by":"publisher","first-page":"22442","DOI":"10.1074\/jbc.M116.754069","volume":"291","author":"CP Wigington","year":"2016","unstructured":"Wigington, C. P., Morris, K. J., Newman, L. E., et al. (2016). The polyadenosine rna-binding protein, zinc finger cys3his protein 14 (zc3h14), regulates the pre-mrna processing of a key atp synthase subunit mrna*. Journal of Biological Chemistry, 291(43), 22442\u201322459. https:\/\/doi.org\/10.1074\/jbc.M116.754069","journal-title":"Journal of Biological Chemistry"},{"key":"6410_CR72","doi-asserted-by":"publisher","unstructured":"Wu, S., Gao, X., & Carroll, R.J. (2023). Model selection of generalized estimating equation with divergent model size. Statistica Sinica, pp. 1\u201322. https:\/\/doi.org\/10.5705\/ss.202020.0197","DOI":"10.5705\/ss.202020.0197"},{"key":"6410_CR73","doi-asserted-by":"crossref","unstructured":"Yi, G. Y. (2014). Composite likelihood\/pseudolikelihood (pp. 1\u201314). Wiley StatsRef: Statistics Reference Online.","DOI":"10.1002\/9781118445112.stat07855"},{"key":"6410_CR74","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-6640-0","volume-title":"Statistical analysis with measurement error or misclassification: strategy, method and application","author":"GY Yi","year":"2017","unstructured":"Yi, G. Y. (2017). Statistical analysis with measurement error or misclassification: strategy, method and application. Berlin: Springer."},{"issue":"38","key":"6410_CR75","first-page":"1","volume":"19","author":"N Yousefi","year":"2018","unstructured":"Yousefi, N., Lei, Y., Kloft, M., et al. (2018). Local rademacher complexity-based learning guarantees for multi-task learning. Journal of Machine Learning Research, 19(38), 1\u201347.","journal-title":"Journal of Machine Learning Research"},{"issue":"1","key":"6410_CR76","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1111\/j.1467-9868.2005.00532.x","volume":"68","author":"M Yuan","year":"2006","unstructured":"Yuan, M., & Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society Series B, 68(1), 49\u201367.","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"6410_CR77","doi-asserted-by":"crossref","unstructured":"Zhan, X.J., Wang, R., & Kuang, X.R., et\u00a0al. (2023). Elevated expression of myosin vi contributes to breast cancer progression via mapk\/erk signaling pathway. Cellular Signalling, p. 110633.","DOI":"10.1016\/j.cellsig.2023.110633"},{"issue":"12","key":"6410_CR78","doi-asserted-by":"publisher","first-page":"i97","DOI":"10.1093\/bioinformatics\/btq181","volume":"26","author":"K Zhang","year":"2010","unstructured":"Zhang, K., Gray, J. W., & Parvin, B. (2010). Sparse multitask regression for identifying common mechanism of response to therapeutic targets. Bioinformatics, 26(12), i97\u2013i105.","journal-title":"Bioinformatics"},{"issue":"4","key":"6410_CR79","doi-asserted-by":"publisher","first-page":"2359","DOI":"10.1214\/18-AOAS1156","volume":"12","author":"H Zhang","year":"2018","unstructured":"Zhang, H., Liu, D., Zhao, J., et al. (2018). Modeling hybrid traits for comorbidity and genetic studies of alcohol and nicotine co-dependence. The Annals of Applied Statistics, 12(4), 2359\u20132378. https:\/\/doi.org\/10.1214\/18-AOAS1156","journal-title":"The Annals of Applied Statistics"},{"issue":"12","key":"6410_CR80","doi-asserted-by":"publisher","first-page":"3259","DOI":"10.1093\/bioinformatics\/btac286","volume":"38","author":"JZ Zhang","year":"2022","unstructured":"Zhang, J. Z., Xu, W., & Hu, P. (2022). Tightly integrated multiomics-based deep tensor survival model for time-to-event prediction. Bioinformatics, 38(12), 3259\u20133266.","journal-title":"Bioinformatics"},{"key":"6410_CR81","unstructured":"Zhang Y, Yang Q (2017) A survey on multi-task learning. CoRR abs\/1707.08114. arxiv:1707.08114"},{"key":"6410_CR82","first-page":"2541","volume":"7","author":"P Zhao","year":"2006","unstructured":"Zhao, P., & Yu, B. (2006). On model selection consistency of lasso. Journal of Machine Learning Research, 7, 2541\u20132563.","journal-title":"Journal of Machine Learning Research"},{"key":"6410_CR83","doi-asserted-by":"crossref","unstructured":"Zhong, Y., Xu, W., & Gao, X. (2023). HMTL: Heterogeneous Multi-Task Feature Learning. R package version 0.1.0.","DOI":"10.32614\/CRAN.package.HMTL"},{"key":"6410_CR84","doi-asserted-by":"crossref","unstructured":"Zhou, J., Yuan, L., & Liu, J., et\u00a0al. (2011). A multi-task learning formulation for predicting disease progression. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Association for Computing Machinery, New York, NY, USA, KDD \u201911, p 814-822","DOI":"10.1145\/2020408.2020549"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-023-06410-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-023-06410-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-023-06410-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T18:05:23Z","timestamp":1764266723000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-023-06410-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,18]]},"references-count":84,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["6410"],"URL":"https:\/\/doi.org\/10.1007\/s10994-023-06410-0","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,18]]},"assertion":[{"value":"3 May 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 October 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"We declare that all the authors have agreed on the submission of this paper to the Machine Learning journal.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}