{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T15:45:40Z","timestamp":1768664740091,"version":"3.49.0"},"reference-count":67,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"ML4Wireless Center Member Companies","award":["AST-144078"],"award-info":[{"award-number":["AST-144078"]}]},{"name":"ML4Wireless Center Member Companies","award":["ECCS-1343398"],"award-info":[{"award-number":["ECCS-1343398"]}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["AST-144078"],"award-info":[{"award-number":["AST-144078"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["ECCS-1343398"],"award-info":[{"award-number":["ECCS-1343398"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE J. Sel. Areas Inf. Theory"],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1109\/jsait.2020.2984716","type":"journal-article","created":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T21:47:37Z","timestamp":1585691257000},"page":"67-83","source":"Crossref","is-referenced-by-count":52,"title":["Harmless Interpolation of Noisy Data in Regression"],"prefix":"10.1109","volume":"1","author":[{"given":"Vidya","family":"Muthukumar","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9849-3055","authenticated-orcid":false,"given":"Kailas","family":"Vodrahalli","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3505-8483","authenticated-orcid":false,"given":"Vignesh","family":"Subramanian","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9263-7719","authenticated-orcid":false,"given":"Anant","family":"Sahai","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref39","first-page":"1177","article-title":"Random features for large-scale kernel machines","author":"rahimi","year":"2008","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1903070116"},{"key":"ref33","first-page":"2300","article-title":"Overfitting or perfect fitting? risk bounds for classification and regression rules that interpolate","author":"belkin","year":"2018","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref32","first-page":"540","article-title":"To understand deep learning we need to understand kernel learning","author":"belkin","year":"2018","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref31","first-page":"1558","article-title":"Explaining the success of adaboost and random forests as interpolating classifiers","volume":"18","author":"wyner","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref30","author":"wei","year":"2018","journal-title":"On the margin theory of feedforward neural networks"},{"key":"ref37","author":"geiger","year":"2018","journal-title":"The jamming transition as a paradigm to understand the loss landscape of deep neural networks"},{"key":"ref36","author":"rakhlin","year":"2018","journal-title":"Consistency of interpolation with laplace kernels is a high-dimensional phenomenon"},{"key":"ref35","author":"liang","year":"2018","journal-title":"Just interpolate Kernel &#x201C;ridgeless&#x201D; regression can generalize"},{"key":"ref34","first-page":"1611","article-title":"Does data interpolation contradict statistical optimality?","author":"belkin","year":"2019","journal-title":"Proc Int Conf Artif Intell Statist"},{"key":"ref60","first-page":"452","article-title":"Isometries of lp-norm","volume":"101","author":"li","year":"1994","journal-title":"Amer Math Monthly"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.909108"},{"key":"ref61","first-page":"2241","article-title":"Restricted eigenvalue properties for correlated Gaussian designs","volume":"11","author":"raskutti","year":"2010","journal-title":"J Mach Learn Res"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2032726"},{"key":"ref28","first-page":"5947","article-title":"Exploring generalization in deep learning","author":"neyshabur","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1137\/0609045"},{"key":"ref27","author":"golowich","year":"2017","journal-title":"Size-independent sample complexity of neural networks"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1016\/0885-064X(91)90002-F"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2008.01.010"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1024691352"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asr043"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/72.788640"},{"key":"ref1","author":"hastie","year":"2009","journal-title":"The Elements of Statistical Learning Data Mining Inference and Prediction"},{"key":"ref20","author":"gunasekar","year":"2018","journal-title":"Characterizing implicit bias in terms of optimization geometry"},{"key":"ref22","author":"woodworth","year":"2019","journal-title":"Kernel and deep regimes in overparametrized models"},{"key":"ref21","first-page":"3420","article-title":"Convergence of gradient descent on separable data","author":"nacson","year":"2019","journal-title":"Proc Int Conf Artif Intell Statist"},{"key":"ref24","author":"shah","year":"2018","journal-title":"Minimum norm solutions do not always generalize well for over-parameterized problems"},{"key":"ref23","first-page":"4148","article-title":"The marginal value of adaptive gradient methods in machine learning","author":"wilson","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref26","first-page":"6240","article-title":"Spectrally-normalized margin bounds for neural networks","author":"bartlett","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref25","first-page":"1376","article-title":"Norm-based capacity control in neural networks","author":"neyshabur","year":"2015","journal-title":"Proc Conf Learn Theory"},{"key":"ref50","first-page":"1","article-title":"Compressive sensing and structured random matrices","volume":"9","author":"rauhut","year":"2011","journal-title":"Theoretical Foundations and Numerical Methods for Sparse Recovery"},{"key":"ref51","author":"belkin","year":"2018","journal-title":"Reconciling modern machine learning and the bias-variance trade-off"},{"key":"ref59","author":"bertsimas","year":"1997","journal-title":"Introduction to Linear Optimization"},{"key":"ref58","author":"belkin","year":"2018","journal-title":"Does data interpolation contradict statistical optimality&#x0192;"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693335"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1214\/15-AOS1337"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2146090"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS620"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1214\/17-AOS1670"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2104512"},{"key":"ref10","author":"mitra","year":"2019","journal-title":"Understanding overfitting peaks in generalization error Analytical risk curves for L? and L? penalized interpolation"},{"key":"ref11","author":"neyshabur","year":"2014","journal-title":"In search of the real inductive bias On the role of implicit regularization in deep learning"},{"key":"ref40","first-page":"9","article-title":"Random design analysis of ridge regression","author":"hsu","year":"2012","journal-title":"Proc Conf Learn Theory"},{"key":"ref12","first-page":"242","article-title":"A convergence theory for deep learning via over-parameterization","author":"allen-zhu","year":"2019","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref13","author":"allen-zhu","year":"2018","journal-title":"Learning and generalization in overparameterized neural networks going beyond two layers"},{"key":"ref14","author":"azizan","year":"2019","journal-title":"Stochastic mirror descent on overparameterized nonlinear models Convergence implicit regularization and generalization"},{"key":"ref15","first-page":"3036","article-title":"On the global convergence of gradient descent for over-parameterized models using optimal transport","author":"chizat","year":"2018","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref16","author":"du","year":"2018","journal-title":"Gradient descent provably optimizes over-parameterized neural networks"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1806579115"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2018.2854560"},{"key":"ref19","first-page":"2822","article-title":"The implicit bias of gradient descent on separable data","volume":"19","author":"soudry","year":"2018","journal-title":"J Mach Learn Res"},{"key":"ref4","author":"zhang","year":"2016","journal-title":"Understanding deep learning requires rethinking generalization"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1214\/009053605000000282"},{"key":"ref6","author":"hastie","year":"2019","journal-title":"Surprises in high-dimensional ridgeless least squares interpolation"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1201\/9781420035933"},{"key":"ref8","author":"bartlett","year":"2019","journal-title":"Benign overfitting in linear regression"},{"key":"ref7","author":"belkin","year":"2019","journal-title":"Two models of double descent for weak features"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1017\/9781108627771"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2019.8849398"},{"key":"ref46","author":"mei","year":"2019","journal-title":"The generalization error of random features regression Precise asymptotics and double descent curve"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1137\/S003614450037906X"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-5849(01)80010-3"},{"key":"ref47","author":"vershynin","year":"2010","journal-title":"Introduction to the Non-Asymptotic Analysis of Random Matrices"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2059891"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2032816"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2173241"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/ACSSC.1993.342465"}],"container-title":["IEEE Journal on Selected Areas in Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/8700143\/8768428\/9051968-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/8700143\/8768428\/09051968.pdf?arnumber=9051968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T13:17:32Z","timestamp":1651065452000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9051968\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5]]},"references-count":67,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/jsait.2020.2984716","relation":{},"ISSN":["2641-8770"],"issn-type":[{"value":"2641-8770","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5]]}}}