{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T07:21:20Z","timestamp":1778311280691,"version":"3.51.4"},"reference-count":103,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"9","license":[{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100008047","name":"Fellowship in Digital Health from the Center for Machine Learning and Health at Carnegie Mellon University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008047","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008047","name":"Dowd Fellowship from the College of Engineering, Carnegie Mellon University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008047","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Philip and Marsha Dowd for their financial support and encouragement"},{"name":"K&L Gates Presidential Fellowship in Ethics and Computational Technologies"},{"DOI":"10.13039\/100000001","name":"NSF CAREER Award","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1109\/tit.2020.2987806","type":"journal-article","created":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T21:31:06Z","timestamp":1586899866000},"page":"5456-5491","source":"Crossref","is-referenced-by-count":15,"title":["Information Flow in Computational Systems"],"prefix":"10.1109","volume":"66","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0752-1506","authenticated-orcid":false,"given":"Praveen","family":"Venkatesh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6500-2627","authenticated-orcid":false,"given":"Sanghamitra","family":"Dutta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7651-7776","authenticated-orcid":false,"given":"Pulkit","family":"Grover","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.3389\/fnsys.2015.00175"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.conb.2012.11.010"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005268"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/S1535-6108(02)00133-2"},{"key":"ref31","author":"peters","year":"2017","journal-title":"Elements of Causal Inference Foundations and Learning Algorithms"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511803161"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1089\/brain.2011.0008"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2017.8007096"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2015.7447102"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2016.2615179"},{"key":"ref28","author":"samuels","year":"2018","journal-title":"Encyclopedia of Clinical Neuropsychology"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bioeng.7.060804.100435"},{"key":"ref29","article-title":"A complexity theory for VLSI","author":"thompson","year":"1980"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.tins.2007.05.004"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0173(99)00049-1"},{"key":"ref21","first-page":"353","article-title":"Microcircuitry of the direct and indirect pathways of the basal ganglia","volume":"86","author":"smith","year":"1998","journal-title":"Neuroscience"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1111\/j.0013-9580.2004.26104.x"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.5295-07.2008"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-21575-1_8"},{"key":"ref101","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOS1145"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.conb.2003.11.001"},{"key":"ref100","doi-asserted-by":"publisher","DOI":"10.1142\/S0219525908001465"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2009.09.073"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1704663114"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2015.7447069"},{"key":"ref57","first-page":"1898","article-title":"Discovering temporal causal relations from subsampled data","volume":"37","author":"gong","year":"2015","journal-title":"Proceedings of the 32nd Intl Conf on Machine Learning"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.75.031123"},{"key":"ref55","first-page":"1","article-title":"Testing for Granger causality in the presence of measurement errors","volume":"3","author":"andersson","year":"2005","journal-title":"Economics Bulletin"},{"key":"ref54","article-title":"In reply to Faes et al. and Barnett et al. regarding &#x2018;A study of problems encountered in Granger causality analysis from a neuroscience perspective","author":"stokes","year":"2017","journal-title":"arXiv 1709 10248"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.12688\/f1000research.12694.1"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2018.05.067"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.2307\/1912791"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0308538101"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-018-0527-y"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.5419-11.2012"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0507062103"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511619632"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/18.850663"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2009.09.036"},{"key":"ref9","article-title":"Actions can speak more clearly than words","author":"grover","year":"2010"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.85.461"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2013.2267934"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.0060315"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1007\/PL00007990"},{"key":"ref42","first-page":"303","article-title":"Causality, feedback and directed information","author":"massey","year":"1990","journal-title":"Proc Int Symp Inf Theory Appl (ISITA)"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2010.02.059"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2478440"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-010-0247-2"},{"key":"ref73","author":"cover","year":"2012","journal-title":"Elements of Information Theory"},{"key":"ref72","first-page":"111","article-title":"Synergy and redundancy among brain cells of behaving monkeys","author":"gat","year":"1999","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1523\/ENEURO.0052-18.2018"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.5319-04.2005"},{"key":"ref76","first-page":"804","article-title":"Kernel-based conditional independence test and application in causal discovery","author":"zhang","year":"2011","journal-title":"Proc 27th Conf Uncertainty Artificial Intell"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS770"},{"key":"ref74","author":"cormen","year":"2009","journal-title":"Introduction to Algorithms"},{"key":"ref75","author":"bergsma","year":"2004","journal-title":"Testing Conditional Independence for Continuous Random Variables"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.11.006"},{"key":"ref79","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466615000286"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1718154115"},{"key":"ref62","author":"oppenheim","year":"1999","journal-title":"Discrete-Time Signal Processing"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1016\/S1053-8119(03)00202-7"},{"key":"ref63","author":"polyanskiy","year":"2017","journal-title":"Lecture Notes on Information Theory"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1949.tb00928.x"},{"key":"ref65","article-title":"Nonnegative decomposition of multivariate information","author":"williams","year":"2010","journal-title":"arXiv 1004 2515"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.87.012130"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.3390\/e16042161"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.3390\/e20040307"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cortex.2013.05.004"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.23-37-11539.2003"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2019.8849411"},{"key":"ref95","doi-asserted-by":"publisher","DOI":"10.1038\/nrn3381"},{"key":"ref94","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.3874-05.2006"},{"key":"ref93","doi-asserted-by":"publisher","DOI":"10.1177\/1073858406293182"},{"key":"ref92","doi-asserted-by":"publisher","DOI":"10.1021\/ac0693722"},{"key":"ref91","doi-asserted-by":"publisher","DOI":"10.1038\/nrn1536"},{"key":"ref90","doi-asserted-by":"publisher","DOI":"10.1126\/science.1128640"},{"key":"ref103","article-title":"How else can we define information flow in neural circuits?","author":"venkatesh","year":"2020","journal-title":"Proc IEEE Int Symp Inf Theory (ISIT)"},{"key":"ref102","article-title":"Understanding encoding and redundancy in grid cells using partial information decomposition","author":"venkatesh","year":"0"},{"key":"ref98","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1995.tb02031.x"},{"key":"ref99","author":"koller","year":"2009","journal-title":"Probabilistic Graphical Models Principles and Techniques"},{"key":"ref96","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.ps.46.020195.003021"},{"key":"ref97","article-title":"Interactive martingale tests for the global null","author":"duan","year":"2019","journal-title":"arXiv 1909 07339"},{"key":"ref10","article-title":"Active systems with uncertain parameters: An information-theoretic perspective","author":"ranade","year":"2014"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-00596-1_21"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/SP.2016.42"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v34i04.5794"},{"key":"ref14","first-page":"2299","article-title":"Estimating information flow in deep neural networks","author":"goldfeld","year":"2019","journal-title":"Proceedings 36th Int Conf Mach Learn"},{"key":"ref15","article-title":"The information bottleneck method","author":"tishby","year":"2000","journal-title":"arXiv physics\/0004057"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/ITW.2015.7133169"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.1162\/089976603321780272"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198805090.001.0001"},{"key":"ref81","article-title":"The hardness of conditional independence testing and the generalised covariance measure","author":"shah","year":"2018","journal-title":"arXiv 1804 07203"},{"key":"ref18","first-page":"598","article-title":"Optimal brain damage","author":"lecun","year":"1990","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref84","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.066138"},{"key":"ref19","first-page":"1","article-title":"The lottery ticket hypothesis: Finding sparse, trainable neural networks","author":"frankle","year":"2019","journal-title":"Proc 7th Int Conf Learn Representations ICLR"},{"key":"ref83","first-page":"5986","article-title":"Estimating mutual information for discrete-continuous mixtures","author":"gao","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref80","article-title":"Mimic and classify: A meta-algorithm for Conditional independence testing","author":"sen","year":"2018","journal-title":"arXiv 1806 09708"},{"key":"ref89","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1966.1053879"},{"key":"ref85","first-page":"2537","article-title":"Exponential concentration for mutual information estimation with application to forests","author":"liu","year":"2012","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref86","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0193(1999)8:4<194::AID-HBM4>3.0.CO;2-C"},{"key":"ref87","doi-asserted-by":"publisher","DOI":"10.1038\/35067550"},{"key":"ref88","doi-asserted-by":"publisher","DOI":"10.1080\/00335558008248231"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/18\/9170933\/9067054-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/9170933\/09067054.pdf?arnumber=9067054","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T17:31:28Z","timestamp":1651080688000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9067054\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":103,"journal-issue":{"issue":"9"},"URL":"https:\/\/doi.org\/10.1109\/tit.2020.2987806","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9]]}}}