{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T05:22:11Z","timestamp":1754112131977,"version":"3.40.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001230","name":"Macquarie University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001230","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Handling high-dimensional datasets presents substantial computational challenges, particularly when the number of features far exceeds the number of observations and when features are highly correlated. A modern approach to mitigate these issues is feature screening. In this work, the High-dimensional Ordinary Least-squares Projection (HOLP) feature screening method is advanced by employing adaptive ridge regularization. The impact of the ridge tuning parameter on the Ridge-HOLP method is examined and Adaptive iterative ridge-HOLP (Air-HOLP) is proposed, a data-adaptive advance to Ridge-HOLP where the ridge-regularization tuning parameter is selected iteratively and optimally for better feature screening performance. The proposed method addresses the challenges of tuning parameter selection in high dimensions by offering a computationally efficient and stable alternative to traditional methods like bootstrapping and cross-validation. Air-HOLP is evaluated using simulated data and a prostate cancer genetic dataset. The empirical results demonstrate that Air-HOLP has improved performance over a large range of simulation settings. We provide R codes implementing the Air-HOLP feature screening method and integrating it into existing feature screening methods that utilize the HOLP formula.<\/jats:p>","DOI":"10.1007\/s11222-025-10599-6","type":"journal-article","created":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T06:20:28Z","timestamp":1741328428000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Air-HOLP: adaptive regularized feature screening for high dimensional correlated data"],"prefix":"10.1007","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0397-6266","authenticated-orcid":false,"given":"Ibrahim","family":"Joudah","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3087-8127","authenticated-orcid":false,"given":"Samuel","family":"Muller","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2515-7413","authenticated-orcid":false,"given":"Houying","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,7]]},"reference":[{"issue":"3","key":"10599_CR1","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1080\/03610910701208619","volume":"36","author":"MA Alkhamisi","year":"2007","unstructured":"Alkhamisi, M.A., Shukur, G.: A monte carlo study of recent ridge parameters. Commun. Stat. Simul. Comput. 36(3), 535\u2013547 (2007). https:\/\/doi.org\/10.1080\/03610910701208619","journal-title":"Commun. Stat. Simul. Comput."},{"issue":"3","key":"10599_CR2","doi-asserted-by":"publisher","first-page":"469","DOI":"10.2307\/1267161","volume":"13","author":"DM Allen","year":"1971","unstructured":"Allen, D.M.: Mean square error of prediction as a criterion for selecting variables. Technometrics 13(3), 469\u2013475 (1971). https:\/\/doi.org\/10.2307\/1267161","journal-title":"Technometrics"},{"issue":"1","key":"10599_CR3","doi-asserted-by":"publisher","first-page":"125","DOI":"10.2307\/1267500","volume":"16","author":"DM Allen","year":"1974","unstructured":"Allen, D.M.: The relationship between variable selection and data agumentation and a method for prediction. Technometrics 16(1), 125\u2013127 (1974). https:\/\/doi.org\/10.2307\/1267500","journal-title":"Technometrics"},{"key":"10599_CR4","first-page":"111","volume":"3","author":"FSM Batah","year":"2008","unstructured":"Batah, F.S.M., Ramanathan, T.V., Gore, S.D.: The efficiency of modified jackknife and ridge type regression estimators: a comparison. Surv. Math. Appl. 3, 111\u2013122 (2008)","journal-title":"Surv. Math. Appl."},{"key":"10599_CR5","doi-asserted-by":"publisher","first-page":"1741","DOI":"10.1007\/s00362-017-0894-8","volume":"60","author":"X Chen","year":"2019","unstructured":"Chen, X., Chen, X., Liu, Y.: A note on quantile feature screening via distance correlation. Stat. Pap. 60, 1741\u20131762 (2019). https:\/\/doi.org\/10.1007\/s00362-017-0894-8","journal-title":"Stat. Pap."},{"issue":"7","key":"10599_CR6","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1002\/gepi.21750","volume":"37","author":"E Cule","year":"2013","unstructured":"Cule, E., De Iorio, M.: Ridge regression in prediction problems: automatic choice of the ridge parameter. Genet. Epidemiol. 37(7), 704\u2013714 (2013). https:\/\/doi.org\/10.1002\/gepi.21750","journal-title":"Genet. Epidemiol."},{"issue":"2","key":"10599_CR7","doi-asserted-by":"publisher","first-page":"255","DOI":"10.2307\/1391324","volume":"4","author":"NJ Delaney","year":"1986","unstructured":"Delaney, N.J., Chatterjee, S.: Use of the bootstrap and cross-validation in ridge regression. J. Bus. Econ. Stat. 4(2), 255\u2013262 (1986). https:\/\/doi.org\/10.2307\/1391324","journal-title":"J. Bus. Econ. Stat."},{"issue":"9","key":"10599_CR8","first-page":"447","volume":"4","author":"A Dorugade","year":"2010","unstructured":"Dorugade, A., Kashid, D.: Alternative method for choosing ridge parameter for regression. Appl. Math. Sci. 4(9), 447\u2013456 (2010)","journal-title":"Appl. Math. Sci."},{"issue":"5","key":"10599_CR9","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1111\/j.1467-9868.2008.00674.x","volume":"70","author":"J Fan","year":"2008","unstructured":"Fan, J., Lv, J.: Sure independence screening for ultrahigh dimensional feature space. J. Roy. Stat. Soc. Ser. B (Stat. Methodol.) 70(5), 849\u2013911 (2008). https:\/\/doi.org\/10.1111\/j.1467-9868.2008.00674.x","journal-title":"J. Roy. Stat. Soc. Ser. B (Stat. Methodol.)"},{"key":"10599_CR10","first-page":"2013","volume":"10","author":"J Fan","year":"2009","unstructured":"Fan, J., Samworth, R., Wu, Y.: Ultrahigh dimensional feature selection: beyond the linear model. J. Mach. Learn. Res. 10, 2013\u20132038 (2009)","journal-title":"J. Mach. Learn. Res."},{"issue":"494","key":"10599_CR11","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1198\/jasa.2011.tm09779","volume":"106","author":"J Fan","year":"2011","unstructured":"Fan, J., Feng, Y., Song, R.: Nonparametric independence screening in sparse ultra-high-dimensional additive models. J. Am. Stat. Assoc. 106(494), 544\u2013557 (2011). https:\/\/doi.org\/10.1198\/jasa.2011.tm09779","journal-title":"J. Am. Stat. Assoc."},{"issue":"507","key":"10599_CR12","doi-asserted-by":"publisher","first-page":"1270","DOI":"10.1080\/01621459.2013.879828","volume":"109","author":"J Fan","year":"2014","unstructured":"Fan, J., Ma, Y., Dai, W.: Nonparametric independence screening in sparse ultra-high-dimensional varying coefficient models. J. Am. Stat. Assoc. 109(507), 1270\u20131284 (2014). https:\/\/doi.org\/10.1080\/01621459.2013.879828","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10599_CR13","doi-asserted-by":"publisher","first-page":"215","DOI":"10.2307\/1268518","volume":"21","author":"GH Golub","year":"1979","unstructured":"Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215\u2013223 (1979). https:\/\/doi.org\/10.2307\/1268518","journal-title":"Technometrics"},{"issue":"3","key":"10599_CR14","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1198\/jcgs.2009.08041","volume":"18","author":"P Hall","year":"2009","unstructured":"Hall, P., Miller, H.: Using generalized correlation to effect variable selection in very high dimensional problems. J. Comput. Graph. Stat. 18(3), 533\u2013550 (2009). https:\/\/doi.org\/10.1198\/jcgs.2009.08041","journal-title":"J. Comput. Graph. Stat."},{"issue":"2","key":"10599_CR15","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1080\/03610927508827232","volume":"4","author":"AE Hoerl","year":"1975","unstructured":"Hoerl, A.E., Kannard, R.W., Baldwin, K.F.: Ridge regression: some simulations. Commun. Stat. Theory Methods 4(2), 105\u2013123 (1975). https:\/\/doi.org\/10.1080\/03610927508827232","journal-title":"Commun. Stat. Theory Methods"},{"issue":"1","key":"10599_CR16","doi-asserted-by":"publisher","first-page":"55","DOI":"10.2307\/1271436","volume":"12","author":"AE Hoerl","year":"1970","unstructured":"Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1), 55\u201367 (1970). https:\/\/doi.org\/10.2307\/1271436","journal-title":"Technometrics"},{"key":"10599_CR17","first-page":"109","volume":"22","author":"MH Hura Ahmad","year":"2006","unstructured":"Hura Ahmad, M.H., Adnan, R., Adnan, N.: A comparative study on some methods for handling multicollinearity problems. MATEMATIKA Malays. J. Ind. Appl. Math. 22, 109\u2013119 (2006)","journal-title":"MATEMATIKA Malays. J. Ind. Appl. Math."},{"issue":"2","key":"10599_CR18","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1081\/SAC-120017499","volume":"32","author":"BG Kibria","year":"2003","unstructured":"Kibria, B.G.: Performance of some new ridge regression estimators. Commun. Stat. Simul. Comput. 32(2), 419\u2013435 (2003). https:\/\/doi.org\/10.1081\/SAC-120017499","journal-title":"Commun. Stat. Simul. Comput."},{"issue":"4","key":"10599_CR19","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1080\/03610927608827353","volume":"5","author":"W Lawless","year":"1976","unstructured":"Lawless, W.: A simulation study of ridge and other regression estimators. Commun. Stat. Theory Methods 5(4), 307\u2013323 (1976). https:\/\/doi.org\/10.1080\/03610927608827353","journal-title":"Commun. Stat. Theory Methods"},{"issue":"499","key":"10599_CR20","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1080\/01621459.2012.695654","volume":"107","author":"R Li","year":"2012","unstructured":"Li, R., Zhong, W., Zhu, L.: Feature screening via distance correlation learning. J. Am. Stat. Assoc. 107(499), 1129\u20131139 (2012). https:\/\/doi.org\/10.1080\/01621459.2012.695654","journal-title":"J. Am. Stat. Assoc."},{"issue":"10","key":"10599_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11425-015-5062-9","volume":"58","author":"J Liu","year":"2015","unstructured":"Liu, J., Zhong, W., Li, R.: A selective overview of feature screening for ultrahigh-dimensional data. Sci. China Math. 58(10), 1\u201322 (2015). https:\/\/doi.org\/10.1007\/s11425-015-5062-9","journal-title":"Sci. China Math."},{"issue":"537","key":"10599_CR22","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1080\/01621459.2020.1783274","volume":"117","author":"W Liu","year":"2022","unstructured":"Liu, W., Ke, Y., Liu, J., Li, R.: Model-free feature screening and fdr control with knockoff features. J. Am. Stat. Assoc. 117(537), 428\u2013443 (2022). https:\/\/doi.org\/10.1080\/01621459.2020.1783274","journal-title":"J. Am. Stat. Assoc."},{"key":"10599_CR23","first-page":"293","volume-title":"Variable Selection and Feature Screening","author":"W Liu","year":"2020","unstructured":"Liu, W., Li, R.: Variable Selection and Feature Screening, pp. 293\u2013326. Springer, Berlin (2020)"},{"issue":"4","key":"10599_CR24","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1198\/tas.2011.11052","volume":"65","author":"JG Martinez","year":"2011","unstructured":"Martinez, J.G., Carroll, R.J., M\u00fcller, S., Sampson, J.N., Chatterjee, N.: Empirical performance of cross-validation with oracle methods in a genomics context. Am. Stat. 65(4), 223\u2013228 (2011). https:\/\/doi.org\/10.1198\/tas.2011.11052","journal-title":"Am. Stat."},{"issue":"3","key":"10599_CR25","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1080\/03610918808812690","volume":"17","author":"M Nomura","year":"1988","unstructured":"Nomura, M.: On the almost unbiased ridge regression estimator. Commun. Stat. Simul. Comput. 17(3), 729\u2013743 (1988). https:\/\/doi.org\/10.1080\/03610918808812690","journal-title":"Commun. Stat. Simul. Comput."},{"issue":"526","key":"10599_CR26","doi-asserted-by":"publisher","first-page":"928","DOI":"10.1080\/01621459.2018.1462709","volume":"114","author":"W Pan","year":"2018","unstructured":"Pan, W., Wang, X., Xiao, W., Zhu, H.: A generic sure independence screening procedure. J. Am. Stat. Assoc. 114(526), 928\u2013937 (2018). https:\/\/doi.org\/10.1080\/01621459.2018.1462709","journal-title":"J. Am. Stat. Assoc."},{"key":"10599_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2019.106894","volume":"144","author":"D Qiu","year":"2020","unstructured":"Qiu, D., Ahn, J.: Grouped variable screening for ultra-high dimensional data for linear model. Computat. Stat. Data Anal. 144, 106894 (2020). https:\/\/doi.org\/10.1016\/j.csda.2019.106894","journal-title":"Computat. Stat. Data Anal."},{"key":"10599_CR28","doi-asserted-by":"publisher","first-page":"8287","DOI":"10.1109\/JSTARS.2022.3206886","volume":"15","author":"A Samat","year":"2022","unstructured":"Samat, A., Li, E., Wang, W., Liu, S., Liu, X.: Holp-df: holp based screening ultrahigh dimensional subfeatures in deep forest for remote sensing image classification. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 15, 8287\u20138298 (2022). https:\/\/doi.org\/10.1109\/JSTARS.2022.3206886","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"doi-asserted-by":"publisher","unstructured":"Tomlins, S.A., Mehra, R., Rhodes, D.R., Cao, X., Wang, L., Dhanasekaran, S.M., Kalyana-Sundaram, S., Wei, J.T., Rubin, M.A., Pienta, K.J., et al.: Integrative molecular concept modeling of prostate cancer progression. Nat. Genet. 39(1), 41\u201351 (2006). https:\/\/doi.org\/10.1038\/ng1935","key":"10599_CR29","DOI":"10.1038\/ng1935"},{"issue":"4","key":"10599_CR30","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1080\/10618600.2021.1904962","volume":"30","author":"MA van de Wiel","year":"2021","unstructured":"van de Wiel, M.A., van Nee, M.M., Rauschenberger, A.: Fast cross-validation for multi-penalty high-dimensional ridge regression. J. Comput. Graph. Stat. 30(4), 835\u2013847 (2021). https:\/\/doi.org\/10.1080\/10618600.2021.1904962","journal-title":"J. Comput. Graph. Stat."},{"doi-asserted-by":"publisher","unstructured":"Wang, X., Leng, C.: High dimensional ordinary least squares projection for screening variables. J. Roy. Stat. Soc. Ser. B (Stat. Methodol.) 78(3), 589\u2013611 (2016). https:\/\/doi.org\/10.1111\/rssb.12127","key":"10599_CR31","DOI":"10.1111\/rssb.12127"},{"doi-asserted-by":"publisher","unstructured":"Wang, X., Leng, C., Boot, T. (2021, 07). Wang and leng,: high-dimensional ordinary least-squares projection for screening variables. J. Roy. Stat. Soc. Ser. B 78, 589\u2013611. J. Roy. Stat. Soc. Ser. B Stat. Methodol. 83(4), 880\u2013881 (2016). https:\/\/doi.org\/10.1111\/rssb.12427","key":"10599_CR32","DOI":"10.1111\/rssb.12427"},{"issue":"1","key":"10599_CR33","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1093\/biomet\/asu068","volume":"102","author":"Y Wu","year":"2015","unstructured":"Wu, Y., Yin, G.: Conditional quantile screening in ultrahigh-dimensional heterogeneous data. Biometrika 102(1), 65\u201376 (2015). https:\/\/doi.org\/10.1093\/biomet\/asu068","journal-title":"Biometrika"},{"key":"10599_CR34","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.csda.2019.06.004","volume":"140","author":"J Zhang","year":"2019","unstructured":"Zhang, J., Chen, X.: Robust sufficient dimension reduction via ball covariance. Comput. Stat. Data Anal. 140, 144\u2013154 (2019). https:\/\/doi.org\/10.1016\/j.csda.2019.06.004","journal-title":"Comput. Stat. Data Anal."},{"key":"10599_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2020.104693","volume":"182","author":"B Zhao","year":"2021","unstructured":"Zhao, B., Liu, X., He, W., Grace, Y.Y.: Dynamic tilted current correlation for high dimensional variable screening. J. Multivar. Anal. 182, 104693 (2021). https:\/\/doi.org\/10.1016\/j.jmva.2020.104693","journal-title":"J. Multivar. Anal."},{"issue":"1","key":"10599_CR36","doi-asserted-by":"publisher","first-page":"69","DOI":"10.5705\/ss.2014.049","volume":"26","author":"W Zhong","year":"2016","unstructured":"Zhong, W., Zhu, L., Li, R., Cui, H.: Regularized quantile regression and robust feature screening for single index models. Stat. Sin. 26(1), 69 (2016). https:\/\/doi.org\/10.5705\/ss.2014.049","journal-title":"Stat. Sin."},{"issue":"496","key":"10599_CR37","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1198\/jasa.2011.tm10563","volume":"106","author":"L-P Zhu","year":"2011","unstructured":"Zhu, L.-P., Li, L., Li, R., Zhu, L.-X.: Model-free feature screening for ultrahigh dimensional data. J. Am. Stat. Assoc. 106(496), 1464\u20131475 (2011). https:\/\/doi.org\/10.1198\/jasa.2011.tm10563","journal-title":"J. Am. Stat. Assoc."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10599-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-025-10599-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10599-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T16:59:56Z","timestamp":1745945996000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-025-10599-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,7]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["10599"],"URL":"https:\/\/doi.org\/10.1007\/s11222-025-10599-6","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2025,3,7]]},"assertion":[{"value":"16 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"There are no conflict of interest to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"63"}}