{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T11:12:15Z","timestamp":1785323535499,"version":"3.55.0"},"reference-count":75,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"8","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CNS-1527754"],"award-info":[{"award-number":["CNS-1527754"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CNS-1718270"],"award-info":[{"award-number":["CNS-1718270"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1553452"],"award-info":[{"award-number":["CCF-1553452"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1617745"],"award-info":[{"award-number":["CCF-1617745"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1651236"],"award-info":[{"award-number":["CCF-1651236"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1705007"],"award-info":[{"award-number":["CCF-1705007"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006785","name":"Google","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006785","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2018,8]]},"DOI":"10.1109\/tit.2018.2807481","type":"journal-article","created":{"date-parts":[[2018,2,19]],"date-time":"2018-02-19T23:32:55Z","timestamp":1519083175000},"page":"5629-5661","source":"Crossref","is-referenced-by-count":73,"title":["Demystifying Fixed &lt;inline-formula&gt; &lt;tex-math notation=\"LaTeX\"&gt;$k$ &lt;\/tex-math&gt; &lt;\/inline-formula&gt;-Nearest Neighbor Information Estimators"],"prefix":"10.1109","volume":"64","author":[{"given":"Weihao","family":"Gao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8975-8306","authenticated-orcid":false,"given":"Sewoong","family":"Oh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3171-8667","authenticated-orcid":false,"given":"Pramod","family":"Viswanath","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref73","author":"owen","year":"2013","journal-title":"Monte Carlo Theory Methods and Examples"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2017.8007086"},{"key":"ref71","author":"moon","year":"2016","journal-title":"Nonparametric ensemble estimation of distributional functionals"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2016.7541476"},{"key":"ref74","author":"david","year":"1970","journal-title":"Order Statistics"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOS1145"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-25388-6"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1561\/0100000072"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.052714"},{"key":"ref32","first-page":"397","article-title":"Nonparametric von mises estimators for entropies, divergences and mutual informations","author":"kandasamy","year":"2015","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/BF00057735"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.899533"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.838380"},{"key":"ref36","author":"ver steeg","year":"2015","journal-title":"The information sieve"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2015.7447116"},{"key":"ref34","first-page":"577","article-title":"Discovering structure in high-dimensional data through correlation explanation","author":"ver steeg","year":"2014","journal-title":"Proc Neural Inf Process Syst"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2195549"},{"key":"ref62","first-page":"1257","article-title":"Estimation of information theoretic measures for continuous random variables","author":"p\u00e9rez-cruz","year":"2009","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref61","first-page":"1849","article-title":"Estimation of R&#x00E9;nyi entropy and mutual information based on generalized nearest-neighbor graphs","author":"p\u00e1l","year":"2010","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref63","doi-asserted-by":"crossref","first-page":"13310","DOI":"10.1103\/PhysRevE.93.013310","article-title":"Nonparametric k-nearest-neighbor entropy estimator","volume":"93","author":"lombardi","year":"2016","journal-title":"Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Top"},{"key":"ref28","first-page":"75","article-title":"Root-n consistent estimators of entropy for densities with unbounded support","volume":"23","author":"tsybakov","year":"1996","journal-title":"Scand J Statist"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1032298287"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1080\/01966324.2003.10737616"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1032298288"},{"key":"ref66","author":"bickel","year":"2009","journal-title":"Monte Carlo and Quasi-Monte Carlo Sampling"},{"key":"ref29","author":"rogers","year":"1998","journal-title":"Hausdorff measures"},{"key":"ref67","first-page":"1217","article-title":"Finite-sample analysis of fixed-k nearest neighbor density functional estimators","author":"singh","year":"2016","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2013.2251456"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2014.6874854"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2462848"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1002\/0471200611.ch12"},{"key":"ref20","author":"acharya","year":"2014","journal-title":"Estimating renyi entropy of discrete distributions"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2412945"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1162\/089976603321780272"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.066138"},{"key":"ref23","first-page":"9","article-title":"Sample estimate of the entropy of a random vector","volume":"23","author":"kozachenko","year":"1987","journal-title":"Problemy Peredachi Inform"},{"key":"ref26","author":"gao","year":"2015","journal-title":"Estimating mutual information by local gaussian approximation"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.026209"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1111\/j.2517-6161.1976.tb01566.x","article-title":"A test for normality based on sample entropy","volume":"38","author":"vasicek","year":"1976","journal-title":"J Roy Statist Soc B Statist Methodol"},{"key":"ref51","first-page":"61","article-title":"Estimating functionals related to a density by a class of statistics based on spacings","volume":"19","author":"van es","year":"1992","journal-title":"Scand J Statist"},{"key":"ref59","article-title":"Locally weighted full covariance Gaussian density estimation","author":"bengio","year":"2003"},{"key":"ref58","first-page":"2555","article-title":"Optimal rates for k-NN density and mode estimation","author":"dasgupta","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref57","author":"kpotufe","year":"2011","journal-title":"Pruning nearest neighbor cluster trees"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1214\/11-EJS606"},{"key":"ref55","article-title":"Discriminatory analysis&#x2014;Nonparametric discrimination: consistency properties","author":"fix","year":"1951"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177700079"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2068870"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1162\/0899766054323026"},{"key":"ref10","first-page":"417","article-title":"Thumbs up or thumbs down?: Semantic orientation applied to unsupervised classification of reviews","author":"turney","year":"2002","journal-title":"Proc Annual Meeting of the Assoc Computational Linguistics"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324452"},{"key":"ref40","author":"makkuva","year":"2016","journal-title":"Equivalence of additive-combinatorial linear inequalities for Shannon entropy and differential entropy"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2016060"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.833360"},{"key":"ref14","author":"wu","year":"2014","journal-title":"Minimax rates of entropy estimation on large alphabets via best polynomial approximation"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.853314"},{"key":"ref16","author":"gao","year":"2014","journal-title":"Efficient estimation of mutual information for strongly dependent variables"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1309933111"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1145\/1993636.1993727"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.2000.892113"},{"key":"ref4","first-page":"27","article-title":"Maximally informative hierarchical representations of high-dimensional data","volume":"1050","author":"ver steeg","year":"2014","journal-title":"Stat"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32717-9_21"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2005.159"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2015.2458316"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/72.298224"},{"key":"ref49","author":"krishnamurthy","year":"2014","journal-title":"Nonparametric estimation of R&#x00E9;nyi divergence and friends"},{"key":"ref7","first-page":"1531","article-title":"Fast binary feature selection with conditional mutual information","volume":"5","author":"fleuret","year":"2004","journal-title":"J Mach Learn Res"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S1361-8415(01)80004-9"},{"key":"ref46","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":"ref45","doi-asserted-by":"publisher","DOI":"10.1007\/BF00773669"},{"key":"ref48","first-page":"1","article-title":"Generalized exponential concentration inequality for R&#x00E9;nyi divergence estimation","author":"singh","year":"2014","journal-title":"Proc 31st Int Conf Mach Learn"},{"key":"ref47","first-page":"3032","article-title":"Exponential concentration of a density functional estimator","author":"singh","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1976.1055550"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3324-9"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.928251"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/18.761291"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielaam\/18\/8410392\/8294268-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/8410392\/08294268.pdf?arnumber=8294268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T22:27:47Z","timestamp":1751408867000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8294268\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8]]},"references-count":75,"journal-issue":{"issue":"8"},"URL":"https:\/\/doi.org\/10.1109\/tit.2018.2807481","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8]]}}}