{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T05:11:53Z","timestamp":1778389913515,"version":"3.51.4"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T00:00:00Z","timestamp":1711929600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T00:00:00Z","timestamp":1711929600000},"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":["Sci. China Inf. Sci."],"published-print":{"date-parts":[[2024,5]]},"DOI":"10.1007\/s11432-021-3724-0","type":"journal-article","created":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T14:03:13Z","timestamp":1712239393000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Granger causal representation learning for groups of time series"],"prefix":"10.1007","volume":"67","author":[{"given":"Ruichu","family":"Cai","sequence":"first","affiliation":[]},{"given":"Yunjin","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Xiaokai","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Wei","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Tom Z. J.","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Zhifeng","family":"Hao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,1]]},"reference":[{"key":"3724_CR1","doi-asserted-by":"publisher","first-page":"6913","DOI":"10.1007\/s00521-019-04161-5","volume":"32","author":"W Chen","year":"2020","unstructured":"Chen W, Cai R C, Hao Z F, et al. Mining hidden non-redundant causal relationships in online social networks. Neural Comput Applic, 2020, 32: 6913\u20136923","journal-title":"Neural Comput Applic"},{"key":"3724_CR2","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.neunet.2013.01.025","volume":"43","author":"R C Cai","year":"2013","unstructured":"Cai R C, Zhang Z J, Hao Z F. Causal gene identification using combinatorial V-structure search. Neural Netw, 2013, 43: 63\u201371","journal-title":"Neural Netw"},{"key":"3724_CR3","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1162\/netn_a_00061","volume":"3","author":"R Sanchez-Romero","year":"2019","unstructured":"Sanchez-Romero R, Ramsey J D, Zhang K, et al. Estimating feedforward and feedback effective connections from fMRI time series: assessments of statistical methods. Netw Neurosci, 2019, 3: 274\u2013306","journal-title":"Netw Neurosci"},{"key":"3724_CR4","first-page":"1709","volume":"11","author":"A Hyv\u00e4rinen","year":"2010","unstructured":"Hyv\u00e4rinen A, Zhang K, Shimizu S, et al. Estimation of a structural vector autoregression model using non-gaussianity. J Mach Learn Res, 2010, 11: 1709\u20131731","journal-title":"J Mach Learn Res"},{"key":"3724_CR5","unstructured":"Peters J, Janzing D, Sch\u00f6lkopf B. Causal inference on time series using restricted structural equation models. In: Proceedings of Advances in Neural Information Processing Systems, 2013. 154\u2013162"},{"key":"3724_CR6","doi-asserted-by":"publisher","first-page":"424","DOI":"10.2307\/1912791","volume":"37","author":"C W J Granger","year":"1969","unstructured":"Granger C W J. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 1969, 37: 424\u2013438","journal-title":"Econometrica"},{"key":"3724_CR7","first-page":"4267","volume":"44","author":"A Tank","year":"2022","unstructured":"Tank A, Covert I, Foti N, et al. Neural Granger causality. IEEE Trans Pattern Anal Mach Intell, 2022, 44: 4267\u20134279","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"3724_CR8","unstructured":"L\u00f6we S, Madras D, Zemel R, et al. Amortized causal discovery: learning to infer causal graphs from time-series data. In: Proceedings of Conference on Causal Learning and Reasoning, 2022. 509\u2013525"},{"key":"3724_CR9","unstructured":"Huang B W, Zhang K, Sanchez-Romero R, et al. Diagnosis of autism spectrum disorder by causal influence strength learned from resting-state fMRI data. 2019. ArXiv:1902.10073"},{"key":"3724_CR10","doi-asserted-by":"crossref","unstructured":"Entner D, Hoyer P O. Estimating a causal order among groups of variables in linear models. In: Proceedings of International Conference on Artificial Neural Networks, 2012. 84\u201391","DOI":"10.1007\/978-3-642-33266-1_11"},{"key":"3724_CR11","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.ijar.2017.05.006","volume":"88","author":"P Parviainen","year":"2017","unstructured":"Parviainen P, Kaski S. Learning structures of Bayesian networks for variable groups. Int J Approximate Reason, 2017, 88: 110\u2013127","journal-title":"Int J Approximate Reason"},{"key":"3724_CR12","volume-title":"Causation, Prediction, and Search","author":"P Spirtes","year":"2000","unstructured":"Spirtes P, Glymour C N, Scheines R, et al. Causation, Prediction, and Search. Cambridge: MIT Press, 2000"},{"key":"3724_CR13","unstructured":"Zhang K, Huang B W, Sch\u00f6lkopf B, et al. Towards robust and specific causal discovery from FMRI. 2015. ArXiv:1509.08056"},{"key":"3724_CR14","first-page":"967","volume":"9","author":"T J Chu","year":"2008","unstructured":"Chu T J, Glymour C. Search for additive nonlinear time series causal models. J Mach Learn Res, 2008, 9: 967\u2013991","journal-title":"J Mach Learn Res"},{"key":"3724_CR15","doi-asserted-by":"publisher","first-page":"4996","DOI":"10.1126\/sciadv.aau4996","volume":"5","author":"J Runge","year":"2019","unstructured":"Runge J, Nowack P, Kretschmer M, et al. Detecting and quantifying causal associations in large nonlinear time series datasets. Sci Adv, 2019, 5: 4996","journal-title":"Sci Adv"},{"key":"3724_CR16","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.neuroimage.2013.06.056","volume":"83","author":"S Ashrafulla","year":"2013","unstructured":"Ashrafulla S, Haldar J P, Joshi A A, et al. Canonical Granger causality between regions of interest. NeuroImage, 2013, 83: 189\u2013199","journal-title":"NeuroImage"},{"key":"3724_CR17","unstructured":"Pamfil R, Sriwattanaworachai N, Desai S, et al. Dynotears: structure learning from time-series data. In: Proceedings of International Conference on Artificial Intelligence and Statistics, 2020. 1595\u20131605"},{"key":"3724_CR18","doi-asserted-by":"publisher","first-page":"524","DOI":"10.3389\/fgene.2019.00524","volume":"10","author":"C Glymour","year":"2019","unstructured":"Glymour C, Zhang K, Spirtes P. Review of causal discovery methods based on graphical models. Front Genet, 2019, 10: 524","journal-title":"Front Genet"},{"key":"3724_CR19","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1109\/JPROC.2021.3058954","volume":"109","author":"B Scholkopf","year":"2021","unstructured":"Scholkopf B, Locatello F, Bauer S, et al. Toward causal representation learning. Proc IEEE, 2021, 109: 612\u2013634","journal-title":"Proc IEEE"},{"key":"3724_CR20","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1016\/j.neuroimage.2010.01.099","volume":"58","author":"D Marinazzo","year":"2011","unstructured":"Marinazzo D, Liao W, Chen H F, et al. Nonlinear connectivity by Granger causality. NeuroImage, 2011, 58: 330\u2013338","journal-title":"NeuroImage"},{"key":"3724_CR21","doi-asserted-by":"publisher","first-page":"3918","DOI":"10.1109\/TSP.2009.2021636","volume":"57","author":"Y O Li","year":"2009","unstructured":"Li Y O, Adali T, Wang W, et al. Joint blind source separation by multiset canonical correlation analysis. IEEE Trans Signal Process, 2009, 57: 3918\u20133929","journal-title":"IEEE Trans Signal Process"},{"key":"3724_CR22","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter S, Schmidhuber J. Long short-term memory. Neural Comput, 1997, 9: 1735\u20131780","journal-title":"Neural Comput"},{"key":"3724_CR23","unstructured":"Ng I, Zhu S Y, Chen Z T, et al. A graph autoencoder approach to causal structure learning. 2019. ArXiv:1911.07420"},{"key":"3724_CR24","unstructured":"Gong P H, Zhang C S, Lu Z S, et al. A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems. In: Proceedings of International Conference on Machine Learning, 2013. 37\u201345"},{"key":"3724_CR25","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.jneumeth.2013.10.018","volume":"223","author":"L Barnett","year":"2014","unstructured":"Barnett L, Seth A K. The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference. J Neurosci Methods, 2014, 223: 50\u201368","journal-title":"J Neurosci Methods"},{"key":"3724_CR26","doi-asserted-by":"publisher","first-page":"043105","DOI":"10.1063\/1.3496397","volume":"20","author":"A Karimi","year":"2010","unstructured":"Karimi A, Paul M R. Extensive chaos in the Lorenz-96 model. Chaos-An Interdisc J Nonlinear Sci, 2010, 20: 043105","journal-title":"Chaos-An Interdisc J Nonlinear Sci"},{"key":"3724_CR27","unstructured":"Tank A, Cover I, Foti N J, et al. An interpretable and sparse neural network model for nonlinear Granger causality discovery. 2017. ArXiv:1711.08160"},{"key":"3724_CR28","doi-asserted-by":"publisher","first-page":"152","DOI":"10.3389\/fnins.2012.00152","volume":"6","author":"K B Nooner","year":"2012","unstructured":"Nooner K B, Colcombe S J, Tobe R H, et al. The NKI-rockland sample: a model for accelerating the pace of discovery science in psychiatry. Front Neurosci, 2012, 6: 152","journal-title":"Front Neurosci"},{"key":"3724_CR29","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1006\/nimg.1998.0395","volume":"9","author":"A M Dale","year":"1999","unstructured":"Dale A M, Fischl B, Sereno M I. Cortical surface-based analysis: I. segmentation and surface reconstruction. NeuroImage, 1999, 9: 179\u2013194","journal-title":"NeuroImage"},{"key":"3724_CR30","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1006\/nimg.1998.0396","volume":"9","author":"B Fischl","year":"1999","unstructured":"Fischl B, Sereno M I, Dale A M. Cortical surface-based analysis: II. ination, attening, and a surface-based coordinate system. NeuroImage, 1999, 9: 195\u2013207","journal-title":"NeuroImage"},{"key":"3724_CR31","doi-asserted-by":"publisher","first-page":"14","DOI":"10.3389\/fninf.2014.00014","volume":"8","author":"A Abraham","year":"2014","unstructured":"Abraham A, Pedregosa F, Eickenberg M, et al. Machine learning for neuroimaging with scikit-learn. Front Neuroinform, 2014, 8: 14","journal-title":"Front Neuroinform"},{"key":"3724_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neuroimage.2010.06.010","volume":"53","author":"C Destrieux","year":"2010","unstructured":"Destrieux C, Fischl B, Dale A, et al. Automatic parcellation of human cortical gyri and sulci using standard anatomical nomenclature. NeuroImage, 2010, 53: 1\u201315","journal-title":"NeuroImage"},{"key":"3724_CR33","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.3389\/fpsyg.2015.01051","volume":"6","author":"E A Garza-Villarreal","year":"2015","unstructured":"Garza-Villarreal E A, Jiang Z, Vuust P, et al. Music reduces pain and increases resting state fMRI BOLD signal amplitude in the left angular gyrus in fibromyalgia patients. Front Psychol, 2015, 6: 1051","journal-title":"Front Psychol"},{"key":"3724_CR34","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1007\/s11682-018-0017-8","volume":"13","author":"X Tan","year":"2019","unstructured":"Tan X, Liang Y, Zeng H, et al. Altered functional connectivity of the posterior cingulate cortex in type 2 diabetes with cognitive impairment. Brain Imag Behav, 2019, 13: 1699\u20131707","journal-title":"Brain Imag Behav"},{"key":"3724_CR35","doi-asserted-by":"publisher","first-page":"280","DOI":"10.3389\/fnagi.2014.00280","volume":"6","author":"W F Cao","year":"2014","unstructured":"Cao W F, Luo C, Zhu B, et al. Resting-state functional connectivity in anterior cingulate cortex in normal aging. Front Aging Neurosci, 2014, 6: 280","journal-title":"Front Aging Neurosci"},{"key":"3724_CR36","doi-asserted-by":"publisher","first-page":"1493","DOI":"10.1097\/MD.0000000000001493","volume":"94","author":"W B Guo","year":"2015","unstructured":"Guo W B, Liu F, Xiao C Q, et al. Increased causal connectivity related to anatomical alterations as potential endophenotypes for schizophrenia. Medicine, 2015, 94: 1493","journal-title":"Medicine"}],"container-title":["Science China Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-021-3724-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11432-021-3724-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-021-3724-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T19:52:42Z","timestamp":1750362762000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11432-021-3724-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,1]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["3724"],"URL":"https:\/\/doi.org\/10.1007\/s11432-021-3724-0","relation":{},"ISSN":["1674-733X","1869-1919"],"issn-type":[{"value":"1674-733X","type":"print"},{"value":"1869-1919","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,1]]},"assertion":[{"value":"12 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"152103"}}