{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T03:08:15Z","timestamp":1790651295713,"version":"4.1.0"},"reference-count":87,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T00:00:00Z","timestamp":1592611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as K-fold cross-validation suffer from large biases. Motivated by the low bias of the leave-one-out cross-validation method, we propose a computationally efficient closed form approximate leave-one-out formula ALO for a large class of regularized estimators. Given the regularized estimate, calculating ALO requires a minor computational overhead. With minor assumptions about the data-generating process, we obtain a finite sample upper bound for the difference between leave-one-out cross-validation and approximate leave-one-out cross-validation, |LO\u2212ALO|. Our theoretical analysis illustrates that |LO\u2212ALO|\u21920 with overwhelming probability, when n, p \u2192 \u221e, where the dimension p of the feature vectors may be comparable with or even greater than the number of observations, n. Despite the high dimensionality of the problem, our theoretical results do not require any sparsity assumption on the vector of regression coefficients. Our extensive numerical experiments show that |LO\u2212ALO| decreases as n and p increase, revealing the excellent finite sample performance of approximate leave-one-out cross-validation. We further illustrate the usefulness of our proposed out-of-sample risk estimation method by an example of real recordings from spatially sensitive neurons (grid cells) in the medial entorhinal cortex of a rat.<\/jats:p>","DOI":"10.1111\/rssb.12374","type":"journal-article","created":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T15:27:17Z","timestamp":1592666837000},"page":"965-996","source":"Crossref","is-referenced-by-count":36,"title":["A Scalable Estimate of the Out-of-Sample Prediction Error via Approximate Leave-One-Out Cross-Validation"],"prefix":"10.1093","volume":"82","author":[{"given":"Kamiar Rahnama","family":"Rad","sequence":"first","affiliation":[{"name":"City University of New York \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arian","family":"Maleki","sequence":"additional","affiliation":[{"name":"Columbia University , New York , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,6,20]]},"reference":[{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"3260","DOI":"10.1162\/neco_a_01021","article-title":"Capturing the dynamical repertoire of single neurons with generalized linear models","volume":"29","author":"Alison","year":"2017","journal-title":"Neurl Computn"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1080\/00401706.1974.10489157","article-title":"The relationship between variable selection and data augmentation and a method for prediction","volume":"16","author":"Allen","year":"1974","journal-title":"Technometrics"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1109\/TIT.2011.2174612","article-title":"The lasso risk for gaussian matrices","volume":"58","author":"Bayati","year":"2012","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"14563","DOI":"10.1073\/pnas.1307845110","article-title":"Optimal m-estimation in high-dimensional regression","volume":"110","author":"Bean","year":"2013","journal-title":"Proc. Natn. Acad. Sci."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780199535255.001.0001","volume-title":"Concentration Inequalities: a Nonasymptotic Theory of Independence","author":"Boucheron","year":"2013"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"Boyd","year":"2004"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1080\/01621459.1983.10477941","article-title":"How many variables should be entered in a regression equation?","volume":"78","author":"Breiman","year":"1983","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"12261","DOI":"10.1073\/pnas.201409398","article-title":"An analysis of neural receptive field plasticity by point process adaptive filtering","volume":"98","author":"Brown","year":"2001","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/0047-259X(90)90083-T","article-title":"Estimation of generalized additive models","volume":"32","author":"Burman","year":"1990","journal-title":"J. Multiv. Anal."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1038\/nn.3304","article-title":"Memory, navigation and theta rythm in the hippocampal-entorhinal system","volume":"16","author":"Buzsaki","year":"2013","journal-title":"Nat. Neursci."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s10994-008-5055-9","article-title":"Efficient approximate leave-one-out cross-validation for kernel logistic regression","volume":"71","author":"Cawley","year":"2008","journal-title":"Mach. Learn."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"191","DOI":"10.2307\/2347628","article-title":"Ridge estimators in logistic regression","volume":"41","author":"le Cessie","year":"1992","journal-title":"Appl. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF01404567","article-title":"Estimating the correct degree of smoothing by the method of generalized cross-validation","volume":"31","author":"Craven","year":"1979","journal-title":"Numer. Math."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1016\/j.neunet.2009.02.004","article-title":"Methods for estimating neural firing rates, and their application to brain-machine interface","volume":"22","author":"Cunningham","year":"2009","journal-title":"Neurl Netwrks"},{"key":"2023022408365471300_","volume-title":"In Advances in Neural Information Processing Systems 20","author":"Cunningham","year":"2008"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"2672","DOI":"10.1152\/jn.00343.2007","article-title":"Analysis of between-trial and within-trial neural spiking dynamics","volume":"99","author":"Czanner","year":"2008","journal-title":"J. Neurphysiol."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/B978-0-12-438660-0.50024-8","volume-title":"In Curves and Surfaces","author":"Deshpande","year":"1991"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1093\/biomet\/88.4.1055","article-title":"Bayesian curve fitting with free-knot splines","volume":"88","author":"DiMatteo","year":"2001","journal-title":"Biometrika"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1214\/17-AOS1549","article-title":"High-dimensional asymptotics of prediction: ridge regression and classification","volume":"46","author":"Dobriban","year":"2018","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","first-page":"6920","volume-title":"IEEE Trans. Inform. Theory","author":"Donoho","year":"2011"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1007\/s00440-015-0675-z","article-title":"High dimensional robust m-estimation: asymptotic variance via approximate message passing","volume":"166","author":"Donoho","year":"2016","journal-title":"Probab. Theory Reltd Flds"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"18914","DOI":"10.1073\/pnas.0909892106","article-title":"Message passing algorithms for compressed sensing","volume":"106","author":"Donoho","year":"2009","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023022408365471300_","first-page":"3475","article-title":"Fast approximation of matrix coherence and statistical leverage","volume":"13","author":"Drineas","year":"2012","journal-title":"J. Mach. Learn. Res."},{"issue":"no. 2","key":"2023022408365471300_","article-title":"Correlations and functional connections in a population of grid cells","volume":"11","author":"Dunn","year":"2015","journal-title":"PLOS Computnl Biol."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1080\/01621459.1983.10477973","article-title":"Estimating the error rate of a prediction rule: improvement on cross-validation","volume":"78","author":"Efron","year":"1983","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1080\/01621459.1986.10478291","article-title":"How biased is the apparent error rate of a prediction rule?","volume":"81","author":"Efron","year":"1986","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s00440-016-0754-9","article-title":"On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators","volume":"170","author":"El Karoui","year":"2018","journal-title":"Probab. Theory Reltd Flds"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"14557","DOI":"10.1073\/pnas.1307842110","article-title":"On robust regression with high-dimensional predictors","volume":"110","author":"El Karoui","year":"2013","journal-title":"Proc. Natn. Acad. Sci. USA"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1080\/00401706.1993.10485033","article-title":"A statistical view of some chemometric regression tools (with discussion)","volume":"35","author":"Frank","year":"1993","journal-title":"Technometrics"},{"key":"2023022408365471300_","first-page":"1","article-title":"Regularization paths for generalized linear models via coordinate descent","volume":"33","author":"Friedman","year":"2010","journal-title":"J. Statist. Softwr"},{"key":"2023022408365471300_","first-page":"213","volume-title":"In Advances in Neural Information Processing Systems 14","author":"Gao","year":"2002"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1080\/01621459.1975.10479865","article-title":"The predictive sample reuse method with applications","volume":"70","author":"Geisser","year":"1975","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1214\/aos\/1030563988","article-title":"Asymptotic comparison of (partial) cross-validation, GCV and randomized GCV in nonparametric regression","volume":"26","author":"Girard","year":"1998","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1080\/00401706.1979.10489751","article-title":"Generalized cross-validation as a method for choosing a good ridge parameter","volume":"21","author":"Golub","year":"1979","journal-title":"Technometrics"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0893-6080(88)90023-8","article-title":"Analysis of hidden units in a layered network trained to classify sonar targets","volume":"1","author":"Gorman","year":"1988","journal-title":"Neurl Netwrks"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/10618600.1992.10477012","article-title":"Cross-validating non-Gaussian data","volume":"1","author":"Gu","year":"1992","journal-title":"J. Computnl Graph. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1198\/106186001317114992","article-title":"Cross-validating non-Gaussian data: generalized approximate cross-validation revisited","volume":"10","author":"Gu","year":"2001","journal-title":"J. Computnl Graph. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1038\/nature03721","article-title":"Microstructure of a spatial map in the enthorhinal cortex","volume":"436","author":"Hafting","year":"2005","journal-title":"Nature"},{"key":"2023022408365471300_","volume-title":"alocv: approximate leave-one-out risk estimation","author":"He","year":"2018"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1093\/biomet\/76.2.297","article-title":"Regression and time series model selection in small samples","volume":"76","author":"Hurvich","year":"1989","journal-title":"Biometrika"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1152\/jn.00648.2004","article-title":"Statistical issues in the analysis of neuronal data","volume":"94","author":"Kass","year":"2005","journal-title":"J. Neurphysiol."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1038\/nn.3606","article-title":"Molecular drivers and cortical spread of lateral entorhinal cortex dysfunction in preclinical Alzheimer\u2019s disease","volume":"17","author":"Khan","year":"2014","journal-title":"Nat. Neursci."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"661","DOI":"10.3150\/08-BEJ127","article-title":"Evaluation and selection of models for out-of-sample prediction when the sample size is small relative to the complexity of the data-generating process","volume":"14","author":"Leeb","year":"2008","journal-title":"Bernoulli"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"2838","DOI":"10.1214\/08-AOS660","article-title":"Conditional predictive inference post model selection","volume":"37","author":"Leeb","year":"2009","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","first-page":"1570","article-title":"Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV","volume":"28","author":"Lin","year":"2000","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.neuroimage.2010.04.272","article-title":"Gaussian process methods for estimating cortical maps","volume":"56","author":"Macke","year":"2011","journal-title":"NeuroImage"},{"key":"2023022408365471300_","volume-title":"Approximate message passing algorithm for compressed sensing. PhD Thesis.","author":"Maleki","year":"2011"},{"key":"2023022408365471300_","first-page":"661","article-title":"Some comments on Cp","volume":"15","author":"Mallows","year":"1973","journal-title":"Technometrics"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1002\/bimj.201200088","article-title":"Efficient approximate k-fold and leave-one-out cross-validation for ridge regression","volume":"55","author":"Meijer","year":"2013","journal-title":"Biometr. J."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1146\/annurev.neuro.31.061307.090723","article-title":"Place cells, grid cells, and the brain\u2019s spatial representation system","volume":"31","author":"Moser","year":"2008","journal-title":"A. Rev. Neursci."},{"issue":"no. 1635","key":"2023022408365471300_","doi-asserted-by":"crossref","DOI":"10.1098\/rstb.2012.0511","article-title":"Network mechanisms of grid cells","volume":"369","author":"Moser","year":"2014","journal-title":"Phil. Trans. R. Soc. B"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1214\/17-AOS1544","article-title":"Consistent parameter estimation for lasso and approximate message passing","volume":"46","author":"Mousavi","year":"2018","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","first-page":"538","article-title":"High-dimensional generalized linear models and the lasso","volume":"4","author":"Negahban","year":"2012","journal-title":"Statist. Sci."},{"key":"2023022408365471300_","volume-title":"Introductory Lectures on Convex Optimization: a Basic Course","author":"Nesterov","year":"2013"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"3045","DOI":"10.1214\/16-EJS1205","article-title":"On Bayesian robust regression with diverging number of predictors","volume":"10","author":"Nevo","year":"2016","journal-title":"Electron. J. Statist."},{"key":"2023022408365471300_","first-page":"1","article-title":"Cross validation in lasso and its acceleration","volume":"53","author":"Obuchi","year":"2016","journal-title":"J. Statist. Mech. Theory. Expt."},{"key":"2023022408365471300_","first-page":"43","volume-title":"In Advances in Large Margin Classifiers","author":"Opper","year":"2000"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1080\/01621459.1986.10478243","article-title":"Automatic smoothing of regression functions in generalized linear models","volume":"81","author":"O\u2019Sullivan","year":"1986","journal-title":"J. Am. Statist. Ass."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1088\/0954-898X_15_4_002","article-title":"Maximum likelihood estimation of cascade point-process neural encoding models","volume":"15","author":"Paninski","year":"2004","journal-title":"Network"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10827-009-0179-x","article-title":"A new look at state-space models for neural data","volume":"29","author":"Paninski","year":"2010","journal-title":"J. Comput. Neursci."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1162\/NECO_a_00615","article-title":"Bayesian active learning of neural firing rate maps with transformed Gaussian process priors","volume":"26","author":"Park","year":"2014","journal-title":"Neurl Computn"},{"key":"2023022408365471300_","first-page":"53","volume-title":"Bayesian Brain: Probabilistic Approaches to Neural Coding","author":"Pillow","year":"2007"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1080\/10618600.2012.760461","article-title":"Fast Kalman filtering and forward-backward smoothing via low-rank perturbative approach","volume":"23","author":"Pnevmatikakis","year":"2014","journal-title":"J. Computnl Graph. Statist."},{"key":"2023022408365471300_","volume-title":"Glmnet for Matlab","author":"Qian","year":"2013"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"142","DOI":"10.3109\/0954898X.2010.532288","article-title":"Efficient estimation of two-dimensional firing rate surfaces via Gaussian process methods","volume":"21","author":"Rahnama Rad","year":"2010","journal-title":"Computn Neurl Syst."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1146\/annurev-neuro-070815-013824","article-title":"Ten years of grid cells","volume":"39","author":"Rowland","year":"2016","journal-title":"A. Rev. Neursci."},{"key":"2023022408365471300_","first-page":"286","volume-title":"In Proc. Eur. Conf. Machine Learning","author":"Schmidt","year":"2007"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1214\/aos\/1176345632","article-title":"Estimation of the mean of a multivariate normal","volume":"9","author":"Stein","year":"1981","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1038\/nature11649","article-title":"The entorhinal grid map is discretized","volume":"492","author":"Stensola","year":"2012","journal-title":"Nature"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1111\/j.2517-6161.1974.tb00994.x","article-title":"Cross-validatory choice and assessment of statistical predictions. (with discussion)","volume":"36","author":"Stone","year":"1974","journal-title":"J. R. Statist. Soc."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1111\/j.2517-6161.1977.tb01603.x","article-title":"An asymptotic equivalence of choice of model by cross-validation and Akaike\u2019s criterion","volume":"39","author":"Stone","year":"1977","journal-title":"J. R. Statist. Soc."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1214\/16-AOS1521","article-title":"False discoveries occur early on the Lasso path","volume":"45","author":"Su","year":"2017","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Statist. Soc."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1214\/12-AOS1003","article-title":"Degrees of freedom in lasso problems","volume":"40","author":"Tibshirani","year":"2012","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1214\/13-EJS815","article-title":"The lasso problem and uniqueness","volume":"7","author":"Tibshirani","year":"2013","journal-title":"Electron. J. Statist."},{"key":"2023022408365471300_","first-page":"614","article-title":"High-dimensional generalized linear models and the lasso","volume":"2","author":"Van de Geer","year":"2008","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","volume-title":"Asymptotic Statistics","author":"Van der Vaart","year":"2000"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1007\/s11222-016-9696-4","article-title":"High-dimensional generalized linear models and the lasso","volume":"5","author":"Vehtari","year":"2017","journal-title":"Statist. Comput."},{"key":"2023022408365471300_","first-page":"3581","article-title":"Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models","volume":"17","author":"Vehtari","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"3358","DOI":"10.1175\/1520-0493(1995)123<3358:ATONWP>2.0.CO;2","article-title":"Adaptive tuning of numerical weather prediction models: randomized GCV in three- and four-dimensional assimilation","volume":"123","author":"Wahba","year":"1995","journal-title":"Mnthly Weath. Rev."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"2183","DOI":"10.1109\/TIT.2009.2016018","article-title":"Sharp thresholds for high-dimensional and noisy sparsity recovery using ell1-constrained quadratic programming (lasso)","volume":"55","author":"Wainwright","year":"2009","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"3099","DOI":"10.1214\/17-AOS1651","article-title":"Overcoming the limitations of phase transition by higher order analysis of regularization techniques","volume":"46","author":"Weng","year":"2018","journal-title":"Ann. Statist."},{"key":"2023022408365471300_","first-page":"675","article-title":"A generalized approximate cross validation for smoothing splines with non-gaussian data","volume":"6","author":"Xiang","year":"1996","journal-title":"Statist. Sin."},{"key":"2023022408365471300_","first-page":"3517","volume-title":"In Advances in Neural Information Processing Systems 31","author":"Zolrowski","year":"2018"},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/j.1467-9868.2005.00503.x","article-title":"Regularization and variable selection via the elastic net","volume":"67","author":"Zou","year":"2005","journal-title":"J. R. Statist. Soc."},{"key":"2023022408365471300_","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1214\/009053607000000127","article-title":"On the \u201cdegrees of freedom\u201d of the lasso","volume":"35","author":"Zou","year":"2007","journal-title":"Ann. Statist."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12374","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12374","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12374","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/82\/4\/965\/49324008\/jrsssb_82_4_965.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/82\/4\/965\/49324008\/jrsssb_82_4_965.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T01:59:33Z","timestamp":1723082373000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/82\/4\/965\/7056054"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,20]]},"references-count":87,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,6,20]]},"published-print":{"date-parts":[[2020,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12374","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,9]]},"published":{"date-parts":[[2020,6,20]]}}}