{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T23:00:48Z","timestamp":1776121248131,"version":"3.50.1"},"reference-count":43,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T00:00:00Z","timestamp":1776038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["CIF-2102243"],"award-info":[{"award-number":["CIF-2102243"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"NIH","doi-asserted-by":"publisher","award":["1R01GM152812-01"],"award-info":[{"award-number":["1R01GM152812-01"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"NIH","doi-asserted-by":"publisher","award":["UG3NS140730"],"award-info":[{"award-number":["UG3NS140730"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"NIH","doi-asserted-by":"publisher","award":["R01AG080043"],"award-info":[{"award-number":["R01AG080043"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this article, we propose a generalized point process additive model with a scalar response and high-dimensional point process predictors. Our proposal is built upon four key components: a realization of a point process as a random counting measure, a generalized point process regression framework, a new kernel function for random measure through kernel embedding, and a suite of low-dimensional structures including the additive model, reduced basis representation, and sparsity. We develop an efficient penalized likelihood procedure for model estimation, and establish both the estimation consistency and selection consistency of the estimator, while allowing the number of point process predictors to diverge. We illustrate and evaluate our method through simulations and an electronic health record data application.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag061","type":"journal-article","created":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T12:47:52Z","timestamp":1774702072000},"source":"Crossref","is-referenced-by-count":0,"title":["Generalized point process additive models"],"prefix":"10.1093","author":[{"given":"Kuang-Yao","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Statistics, Operations, and Data Science, Temple University , Philadelphia, PA 19122 ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5940-4822","authenticated-orcid":false,"given":"Jiehuan","family":"Sun","sequence":"additional","affiliation":[{"name":"Division of Epidemiology and Biostatistics, University of Illinois , Chicago, IL 60612 ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Statistics, Pennsylvania State University , University Park, PA 16802 ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2962-1989","authenticated-orcid":false,"given":"Lexin","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Epidemiology, University of California, Berkeley , 2121 Berkeley Way, #5302, Berkeley, CA 94720","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2026,4,13]]},"reference":[{"key":"2026041318164431300_qkag061-B1","doi-asserted-by":"publisher","author":"Bach","year":"2009","DOI":"10.48550\/arXiv.0909.0844"},{"key":"2026041318164431300_qkag061-B2","first-page":"1179","article-title":"Consistency of the group lasso and multiple kernel learning","volume":"9","author":"Bach","year":"2008","journal-title":"Journal of Machine Learning Research"},{"key":"2026041318164431300_qkag061-B3","first-page":"1","article-title":"Sparse and low-rank multivariate Hawkes processes","volume":"21","author":"Bacry","year":"2020","journal-title":"Journal of Machine Learning Research"},{"key":"2026041318164431300_qkag061-B4","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1090\/S0002-9947-1973-0336795-3","article-title":"Joint measures and cross-covariance operators","volume":"186","author":"Baker","year":"1973","journal-title":"Transactions of the American Mathematical Society"},{"key":"2026041318164431300_qkag061-B5","doi-asserted-by":"crossref","DOI":"10.1515\/9783110866209","volume-title":"Measure and integration theory","author":"Bauer","year":"2001"},{"key":"2026041318164431300_qkag061-B6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1154-9","volume-title":"Linear processes in function spaces","author":"Bosq","year":"2000"},{"issue":"545","key":"2026041318164431300_qkag061-B7","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1080\/01621459.2022.2102019","article-title":"Latent network structure learning from high-dimensional multivariate point processes","volume":"119","author":"Cai","year":"2024","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2026041318164431300_qkag061-B8","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1214\/17-EJS1251","article-title":"Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process","volume":"11","author":"Chen","year":"2017","journal-title":"Electronic Journal of Statistics"},{"key":"2026041318164431300_qkag061-B9","doi-asserted-by":"publisher","author":"Chouldechova","year":"2015","DOI":"10.48550\/arXiv.1506.03850"},{"key":"2026041318164431300_qkag061-B10","volume-title":"Point processes","author":"Cox","year":"1980"},{"issue":"4","key":"2026041318164431300_qkag061-B11","doi-asserted-by":"publisher","first-page":"2435","DOI":"10.1214\/14-AOAS781","article-title":"Functional response additive model estimation with online virtual stock markets","volume":"8","author":"Fan","year":"2014","journal-title":"The Annals of Applied Statistics"},{"issue":"5","key":"2026041318164431300_qkag061-B12","doi-asserted-by":"publisher","first-page":"2296","DOI":"10.1214\/15-AOS1346","article-title":"Functional additive regression","volume":"43","author":"Fan","year":"2015","journal-title":"Annals of Statistics"},{"issue":"2","key":"2026041318164431300_qkag061-B13","doi-asserted-by":"publisher","first-page":"1133","DOI":"10.1109\/TIT.2021.3126466","article-title":"Cox point process regression","volume":"68","author":"Gajardo","year":"2022","journal-title":"IEEE Transactions on Information Theory"},{"issue":"483","key":"2026041318164431300_qkag061-B14","doi-asserted-by":"publisher","first-page":"1238","DOI":"10.1198\/016214508000000526","article-title":"On consistent nonparametric intensity estimation for inhomogeneous spatial point processes","volume":"103","author":"Guan","year":"2008","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2026041318164431300_qkag061-B15","doi-asserted-by":"publisher","first-page":"83","DOI":"10.3150\/13-BEJ562","article-title":"Lasso and probabilistic inequalities for multivariate point processes","volume":"21","author":"Hansen","year":"2015","journal-title":"Bernoulli"},{"key":"2026041318164431300_qkag061-B16","volume-title":"Generalized additive models","author":"Hastie","year":"1990"},{"issue":"1","key":"2026041318164431300_qkag061-B17","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1093\/biomet\/58.1.83","article-title":"Spectra of some self-exciting and mutually exciting point processes","volume":"58","author":"Hawkes","year":"1971","journal-title":"Biometrika"},{"key":"2026041318164431300_qkag061-B18","doi-asserted-by":"publisher","first-page":"1800","DOI":"10.1214\/14-aoas757","article-title":"A bayesian hierarchical spatial point process model for multi-type neuroimaging meta-analysis","volume":"8","author":"Kang","year":"2014","journal-title":"The Annals of Applied Statistics"},{"issue":"2","key":"2026041318164431300_qkag061-B19","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1111\/rssb.12471","article-title":"Functional structural equation model","volume":"84","author":"Lee","year":"2022","journal-title":"Journal of the Royal Statistical Society Series B"},{"issue":"543","key":"2026041318164431300_qkag061-B20","doi-asserted-by":"publisher","first-page":"1718","DOI":"10.1080\/01621459.2021.2006667","article-title":"Nonparametric functional graphical modelling through functional additive regression operator","volume":"118","author":"Lee","year":"2023","journal-title":"Journal of the American Statistical Association"},{"issue":"524","key":"2026041318164431300_qkag061-B21","doi-asserted-by":"publisher","first-page":"1637","DOI":"10.1080\/01621459.2017.1356726","article-title":"A nonparametric graphical model for functional data with application to brain networks based on fMRI","volume":"113","author":"Li","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2026041318164431300_qkag061-B22","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1214\/16-AOS1475","article-title":"Nonlinear sufficient dimension reduction for functional data","volume":"45","author":"Li","year":"2017","journal-title":"Annals of Statistics"},{"issue":"1","key":"2026041318164431300_qkag061-B23","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1214\/23-aoas1808","article-title":"A partially functional linear regression framework for integrating genetic, imaging, and clinical data","volume":"18","author":"Li","year":"2024","journal-title":"The Annals of Applied Statistics"},{"key":"2026041318164431300_qkag061-B24","doi-asserted-by":"publisher","first-page":"1379","DOI":"10.5705\/ss.202018.0155","article-title":"Inference for generalized partial functional linear regression","volume":"30","author":"Li","year":"2020","journal-title":"Statistica Sinica"},{"issue":"507","key":"2026041318164431300_qkag061-B25","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1080\/01621459.2014.885434","article-title":"Functional principal component analysis of spatiotemporal point processes with applications in disease surveillance","volume":"109","author":"Li","year":"2014","journal-title":"Journal of the American Statistical Association"},{"issue":"490","key":"2026041318164431300_qkag061-B26","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1198\/jasa.2010.tm09313","article-title":"Generalized functional linear models with semiparametric single-index interactions","volume":"105","author":"Li","year":"2010","journal-title":"Journal of the American Statistical Association"},{"issue":"6B","key":"2026041318164431300_qkag061-B27","doi-asserted-by":"publisher","first-page":"3779","DOI":"10.1214\/09-AOS692","article-title":"High-dimensional additive modelling","volume":"37","author":"Meier","year":"2009","journal-title":"Annals of Statistics"},{"key":"2026041318164431300_qkag061-B28","article-title":"Distribution-free distribution regression","author":"P\u00f3czos","year":"2013"},{"key":"2026041318164431300_qkag061-B29","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1111\/j.1467-9868.2009.00718.x","article-title":"Sparse additive models","volume":"71","author":"Ravikumar","year":"2009","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"issue":"3","key":"2026041318164431300_qkag061-B30","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1214\/09-AOS691","article-title":"High-dimensional Ising model selection using l1-regularized logistic regression","volume":"38","author":"Ravikumar","year":"2010","journal-title":"Annals of Statistics"},{"issue":"4","key":"2026041318164431300_qkag061-B31","doi-asserted-by":"publisher","first-page":"1742","DOI":"10.1214\/15-AOS1322","article-title":"Nonparametric inference in generalized functional linear models","volume":"43","author":"Shang","year":"2015","journal-title":"Annals of Statistics"},{"key":"2026041318164431300_qkag061-B32","author":"Silva","year":"2012"},{"key":"2026041318164431300_qkag061-B33","doi-asserted-by":"crossref","DOI":"10.1201\/9781315140919","volume-title":"Density estimation for statistics and data analysis","author":"Silverman","year":"2018"},{"key":"2026041318164431300_qkag061-B34","first-page":"2389","article-title":"Universality, characteristic kernels and RKHS embedding of measures","volume":"12","author":"Sriperumbudur","year":"2011","journal-title":"Journal of Machine Learning Research"},{"issue":"152","key":"2026041318164431300_qkag061-B35","first-page":"1","article-title":"Learning theory for distribution regression","volume":"17","author":"Szab\u00f3","year":"2016","journal-title":"Journal of Machine Learning Research"},{"issue":"542","key":"2026041318164431300_qkag061-B36","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1080\/01621459.2021.1955690","article-title":"Multivariate temporal point process regression","volume":"118","author":"Tang","year":"2023","journal-title":"Journal of the American Statistical Association"},{"key":"2026041318164431300_qkag061-B37","doi-asserted-by":"crossref","DOI":"10.1017\/9781108627771","volume-title":"High-dimensional statistics: A non-asymptotic viewpoint","author":"Wainwright","year":"2019"},{"issue":"192","key":"2026041318164431300_qkag061-B38","first-page":"1","article-title":"Semi-parametric learning of structured temporal point processes","volume":"21","author":"Xu","year":"2020","journal-title":"Journal of Machine Learning Research"},{"issue":"2","key":"2026041318164431300_qkag061-B39","doi-asserted-by":"publisher","DOI":"10.4310\/21-SII688","article-title":"Sparse logistic regression on functional data","volume":"15","author":"Xu","year":"2022","journal-title":"Statistics & Its Interface"},{"key":"2026041318164431300_qkag061-B40","first-page":"2541","article-title":"On model selection consistency of Lasso","volume":"7","author":"Zhao","year":"2006","journal-title":"Journal of Machine Learning Research: JMLR"},{"key":"2026041318164431300_qkag061-B41","first-page":"641","author":"Zhou","year":"2013"},{"issue":"2","key":"2026041318164431300_qkag061-B42","doi-asserted-by":"publisher","first-page":"1441","DOI":"10.3150\/23-BEJ1639","article-title":"Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures","volume":"30","author":"Ziegel","year":"2024","journal-title":"Bernoulli"},{"issue":"2","key":"2026041318164431300_qkag061-B43","doi-asserted-by":"publisher","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":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/advance-article-pdf\/doi\/10.1093\/jrsssb\/qkag061\/68070372\/qkag061.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/advance-article-pdf\/doi\/10.1093\/jrsssb\/qkag061\/68070372\/qkag061.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T22:16:49Z","timestamp":1776118609000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/advance-article\/doi\/10.1093\/jrsssb\/qkag061\/8653277"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,13]]},"references-count":43,"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkag061","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,13]]},"article-number":"qkag061"}}