{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T10:53:08Z","timestamp":1767178388351,"version":"build-2238731810"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009746","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T00:00:00Z","timestamp":1642723200000}}],"reference-count":76,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T00:00:00Z","timestamp":1641772800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN 2019-05888"],"award-info":[{"award-number":["RGPIN 2019-05888"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000024","name":"Canadian Institutes of Health Research","doi-asserted-by":"publisher","award":["PJT-156114"],"award-info":[{"award-number":["PJT-156114"]}],"id":[{"id":"10.13039\/501100000024","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007670","name":"Dalhousie Medical Research Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007670","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>We have built a computational model for individual aging trajectories of health and survival, which contains physical, functional, and biological variables, and is conditioned on demographic, lifestyle, and medical background information. We combine techniques of modern machine learning with an interpretable interaction network, where health variables are coupled by explicit pair-wise interactions within a stochastic dynamical system. Our dynamic joint interpretable network (DJIN) model is scalable to large longitudinal data sets, is predictive of individual high-dimensional health trajectories and survival from baseline health states, and infers an interpretable network of directed interactions between the health variables. The network identifies plausible physiological connections between health variables as well as clusters of strongly connected health variables. We use English Longitudinal Study of Aging (ELSA) data to train our model and show that it performs better than multiple dedicated linear models for health outcomes and survival. We compare our model with flexible lower-dimensional latent-space models to explore the dimensionality required to accurately model aging health outcomes. Our DJIN model can be used to generate synthetic individuals that age realistically, to impute missing data, and to simulate future aging outcomes given arbitrary initial health states.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009746","type":"journal-article","created":{"date-parts":[[2022,1,10]],"date-time":"2022-01-10T13:30:56Z","timestamp":1641821456000},"page":"e1009746","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":18,"title":["Interpretable machine learning for high-dimensional trajectories of aging health"],"prefix":"10.1371","volume":"18","author":[{"given":"Spencer","family":"Farrell","sequence":"first","affiliation":[]},{"given":"Arnold","family":"Mitnitski","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6674-995X","authenticated-orcid":true,"given":"Kenneth","family":"Rockwood","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4264-6809","authenticated-orcid":true,"given":"Andrew D.","family":"Rutenberg","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,1,10]]},"reference":[{"key":"pcbi.1009746.ref001","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.cell.2005.01.027","article-title":"Understanding the odd science of aging","volume":"120","author":"TBL Kirkwood","year":"2005","journal-title":"Cell"},{"key":"pcbi.1009746.ref002","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1016\/j.cell.2013.05.039","article-title":"The hallmarks of aging","volume":"153","author":"C L\u00f3pez-Ot\u00edn","year":"2013","journal-title":"Cell"},{"key":"pcbi.1009746.ref003","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1038\/nature01135","article-title":"Stochastic and genetic factors influence tissue-specific decline in ageing C. elegans","volume":"419","author":"LA Herndon","year":"2002","journal-title":"Nature"},{"key":"pcbi.1009746.ref004","doi-asserted-by":"crossref","first-page":"794","DOI":"10.1038\/419794a","article-title":"The old worm turns more slowly","volume":"419","author":"TBL Kirkwood","year":"2002","journal-title":"Nature"},{"key":"pcbi.1009746.ref005","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.mad.2019.03.007","article-title":"Frailty biomarkers in humans and rodents: Current approaches and future advances","volume":"180","author":"AE Kane","year":"2019","journal-title":"Mechanisms of Ageing and Development"},{"key":"pcbi.1009746.ref006","doi-asserted-by":"crossref","first-page":"e13080","DOI":"10.1111\/acel.13080","article-title":"Measuring biological aging in humans: A quest","volume":"19","author":"L Ferrucci","year":"2020","journal-title":"Aging Cell"},{"issue":"6","key":"pcbi.1009746.ref007","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1093\/gerona\/gls233","article-title":"Modeling the Rate of Senescence: Can Estimated Biological Age Predict Mortality More Accurately Than Chronological Age?","volume":"68","author":"ME Levine","year":"2012","journal-title":"The Journals of Gerontology: Series A"},{"key":"pcbi.1009746.ref008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2318-2-1","article-title":"Frailty, fitness and late-life mortality in relation to chronological and biological age","volume":"2","author":"AB Mitnitski","year":"2002","journal-title":"BMC Geriatrics"},{"key":"pcbi.1009746.ref009","doi-asserted-by":"crossref","first-page":"R115","DOI":"10.1186\/gb-2013-14-10-r115","article-title":"DNA methylation age of human tissues and cell types","volume":"14","author":"S Horvath","year":"2013","journal-title":"Genome Biology"},{"key":"pcbi.1009746.ref010","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1100\/tsw.2001.58","article-title":"Accumulation of deficits as a proxy measure of aging","volume":"1","author":"AB Mitnitski","year":"2001","journal-title":"The Scientific World"},{"issue":"3","key":"pcbi.1009746.ref011","doi-asserted-by":"crossref","first-page":"M146","DOI":"10.1093\/gerona\/56.3.M146","article-title":"Frailty in older adults: Evidence for a phenotype","volume":"56","author":"LP Fried","year":"2001","journal-title":"The Journals of Gerontology: Series A"},{"key":"pcbi.1009746.ref012","first-page":"97","article-title":"Inferring Multidimensional Rates of Aging from Cross-Sectional Data","volume":"89","author":"E Pierson","year":"2019","journal-title":"Proc Mach Learn Res"},{"key":"pcbi.1009746.ref013","article-title":"Identification of a blood test-based biomarker of aging through deep learning of aging trajectories in large phenotypic datasets of mice","author":"K Avchaciov","year":"2020","journal-title":"bioRxiv"},{"key":"pcbi.1009746.ref014","doi-asserted-by":"crossref","first-page":"111403","DOI":"10.1016\/j.mad.2020.111403","article-title":"The potential for complex computational models of aging","volume":"193","author":"S Farrell","year":"2021","journal-title":"Mechanisms of Ageing and Development"},{"key":"pcbi.1009746.ref015","first-page":"3600","article-title":"Efficient learning of continuous-time hidden markov models for disease progression","author":"YY Liu","year":"2015","journal-title":"Advances in Neural Information Processing Systems"},{"key":"pcbi.1009746.ref016","article-title":"A Framework for Individualizing Predictions of Disease Trajectories by Exploiting Multi-Resolution Structure","author":"P Schulam","year":"2015","journal-title":"Advances in Neural Information Processing Systems 28"},{"key":"pcbi.1009746.ref017","author":"AM Alaa","year":"2018","journal-title":"Forecasting Individualized Disease Trajectories using Interpretable Deep Learning"},{"issue":"1","key":"pcbi.1009746.ref018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-019-49656-2","article-title":"Machine learning for comprehensive forecasting of Alzheimer\u2019s Disease progression","volume":"9","author":"CK Fisher","year":"2019","journal-title":"Scientific Reports"},{"key":"pcbi.1009746.ref019","author":"JR Walsh","year":"2020","journal-title":"Generating digital twins with multiple sclerosis using probabilistic neural networks"},{"key":"pcbi.1009746.ref020","first-page":"137","article-title":"Disease-Atlas: Navigating disease trajectories using deep learning","volume":"85","author":"B Lim","year":"2018","journal-title":"Proceeding of Machine Learning Research"},{"key":"pcbi.1009746.ref021","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/j.mbs.2006.11.006","article-title":"Stochastic model for analysis of longitudinal data on aging and mortality","volume":"208","author":"AI Yashin","year":"2007","journal-title":"Mathematical Biosciences"},{"issue":"228","key":"pcbi.1009746.ref022","article-title":"Joint analyses of longitudinal and time-to-event data in research on aging: Implications for predicting health and survival","volume":"2","author":"KG Arbeev","year":"2014","journal-title":"Frontiers in Public Health"},{"issue":"125","key":"pcbi.1009746.ref023","article-title":"stpm: an R package for stochastic process model","volume":"18","author":"IY Zhbannikov","year":"2017","journal-title":"BMC Bioinformatics"},{"key":"pcbi.1009746.ref024","doi-asserted-by":"crossref","first-page":"19833","DOI":"10.1038\/s41598-020-76827-3","article-title":"Generating synthetic aging trajectories with a weighted network model using cross-sectional data","author":"S Farrell","year":"2020","journal-title":"Scientific Reports"},{"key":"pcbi.1009746.ref025","article-title":"English Longitudinal Study of Ageing: Waves 0-8 1998-2017","volume":"5050","author":"S Clemens","year":"2019","journal-title":"UK Data Service 30th Edition"},{"issue":"5","key":"pcbi.1009746.ref026","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1038\/s42256-019-0048-x","article-title":"Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead","volume":"1","author":"C Rudin","year":"2019","journal-title":"Nature Machine Intelligence"},{"key":"pcbi.1009746.ref027","author":"C Rackauckas","year":"2020","journal-title":"Universal Differential Equations for Scientific Machine Learning"},{"issue":"10","key":"pcbi.1009746.ref028","doi-asserted-by":"crossref","first-page":"2318","DOI":"10.1109\/TKDE.2017.2720168","article-title":"Theory-guided data science: A new paradigm for scientific discovery from data","volume":"29","author":"A Karpatne","year":"2017","journal-title":"IEEE Transactions on knowledge and data engineering"},{"key":"pcbi.1009746.ref029","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s10522-017-9684-x","article-title":"Aging, frailty and complex networks","volume":"18","author":"AB Mitnitski","year":"2017","journal-title":"Biogerontology"},{"key":"pcbi.1009746.ref030","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.exger.2017.08.027","article-title":"Unifying aging and frailty through complex dynamical networks","volume":"107","author":"AD Rutenberg","year":"2018","journal-title":"Experimental Gerontology"},{"issue":"8","key":"pcbi.1009746.ref031","article-title":"Genomic data imputation with variational auto-encoders","volume":"9","author":"YL Qiu","year":"2020","journal-title":"GigaScience"},{"key":"pcbi.1009746.ref032","unstructured":"Gong Y, Hajimirsadeghi H, He J, Nawhal M, Durand T, Mori G. Variational Selective Autoencoder. In: Zhang C, Ruiz F, Bui T, Dieng AB, Liang D, editors. Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference. vol. 118 of Proceedings of Machine Learning Research. PMLR; 2020. p. 1\u201317. Available from: http:\/\/proceedings.mlr.press\/\/v118\/\/gong20a.html."},{"key":"pcbi.1009746.ref033","unstructured":"Rezende D, Mohamed S. Variational Inference with Normalizing Flows. In: Bach F, Blei D, editors. Proceedings of the 32nd International Conference on Machine Learning. vol. 37 of Proceedings of Machine Learning Research. Lille, France: PMLR; 2015. p. 1530\u20131538. Available from: http:\/\/proceedings.mlr.press\/v37\/rezende15.html."},{"key":"pcbi.1009746.ref034","first-page":"20","article-title":"Effects of unobserved and partially observed covariate processes on system failure: A review of models and estimation strategies","volume":"12","author":"AI Yashin","year":"1997","journal-title":"Statistical Science"},{"key":"pcbi.1009746.ref035","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.plrev.2012.05.002","article-title":"The quadratic hazard model for analyzing longitudinal data on aging, health, and the life span","volume":"9","author":"AI Yashin","year":"2012","journal-title":"Physics of Life Reviews"},{"issue":"518","key":"pcbi.1009746.ref036","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational Inference: A Review for Statisticians","volume":"112","author":"DM Blei","year":"2017","journal-title":"Journal of the American Statistical Association"},{"key":"pcbi.1009746.ref037","doi-asserted-by":"crossref","first-page":"3927","DOI":"10.1002\/sim.2427","article-title":"A time-dependent discrimination index for survival data","volume":"24","author":"L Antolini","year":"2005","journal-title":"Statistics in Medicine"},{"issue":"3","key":"pcbi.1009746.ref038","first-page":"1","article-title":"mice: Multivariate Imputation by Chained Equations in R","volume":"45","author":"S van Buuren","year":"2011","journal-title":"Journal of Statistical Software, Articles"},{"issue":"1","key":"pcbi.1009746.ref039","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1093\/bioinformatics\/btr597","article-title":"MissForest\u2014non-parametric missing value imputation for mixed-type data","volume":"28","author":"DJ Stekhoven","year":"2011","journal-title":"Bioinformatics"},{"key":"pcbi.1009746.ref040","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1002\/(SICI)1097-0258(19990915\/30)18:17\/18<2529::AID-SIM274>3.0.CO;2-5","article-title":"Assessment and comparison of prognostic classification schemes for survival data","volume":"18","author":"E Graf","year":"1999","journal-title":"Statistics in Medicine"},{"key":"pcbi.1009746.ref041","first-page":"1","article-title":"Effective ways to build and evaluate individual survival distributions","volume":"21","author":"H Haider","year":"2020","journal-title":"Journal of Machine Learning Research"},{"issue":"10","key":"pcbi.1009746.ref042","doi-asserted-by":"crossref","first-page":"2973","DOI":"10.18632\/aging.101603","article-title":"Quantitative characterization of biological age and frailty based on locomotor activity records","volume":"10","author":"TV Pyrkov","year":"2018","journal-title":"Aging"},{"key":"pcbi.1009746.ref043","unstructured":"Lopez-Paz D, Oquab M. Revisiting Classifier Two-Sample Tests. In: 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24\u201326, 2017, Conference Track Proceedings. OpenReview.net; 2017.Available from: https:\/\/openreview.net\/forum?id=SJkXfE5xx."},{"key":"pcbi.1009746.ref044","author":"D Bertolini","year":"2020","journal-title":"Modeling Disease Progression in Mild Cognitive Impairment and Alzheimer\u2019s Disease with Digital Twins"},{"key":"pcbi.1009746.ref045","doi-asserted-by":"crossref","first-page":"032317","DOI":"10.1103\/PhysRevE.97.032317","article-title":"Sparse dynamical Boltzmann machine for reconstructing complex networks with binary dynamics","volume":"97","author":"YZ Chen","year":"2018","journal-title":"Physical Review E"},{"key":"pcbi.1009746.ref046","article-title":"Latent Ordinary Differential Equations for Irregularly-Sampled Time Series","volume":"32","author":"Y Rubanova","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"key":"pcbi.1009746.ref047","first-page":"7377","article-title":"GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series","author":"E De Brouwer","year":"2019","journal-title":"NeurIPS"},{"key":"pcbi.1009746.ref048","author":"J Jordon","year":"2020","journal-title":"Synthetic Data: Opening the data floodgates to enable faster, more directed development of machine learning methods"},{"key":"pcbi.1009746.ref049","unstructured":"https:\/\/zenodo.org\/record\/4733386"},{"key":"pcbi.1009746.ref050","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2202\/1544-6115.1128","article-title":"A general framework for weighted gene co-expression network analysis","volume":"4","author":"B Zhang","year":"2005","journal-title":"Statistical Applications in Genetics and Molecular Biology"},{"key":"pcbi.1009746.ref051","doi-asserted-by":"crossref","first-page":"110747","DOI":"10.1016\/j.exger.2019.110747","article-title":"Network analysis of frailty and aging: Empirical data from the Mexican Health and Aging Study","volume":"128","author":"C Garc\u00eda-Pe\u00f1a","year":"2019","journal-title":"Experimental Gerontology"},{"key":"pcbi.1009746.ref052","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/S0019-9958(63)90092-5","article-title":"Economic processes involving feedback","volume":"6","author":"CWJ Granger","year":"1963","journal-title":"Information and Control"},{"issue":"4","key":"pcbi.1009746.ref053","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1016\/S1053-8119(03)00202-7","article-title":"Dynamic causal modelling","volume":"19","author":"KJ Friston","year":"2003","journal-title":"NeuroImage"},{"key":"pcbi.1009746.ref054","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1016\/j.neuroimage.2017.02.045","article-title":"Dynamic causal modelling revisited","volume":"199","author":"KJ Friston","year":"2019","journal-title":"NeuroImage"},{"key":"pcbi.1009746.ref055","doi-asserted-by":"crossref","unstructured":"Xiao S, Yan J, Yang X, Zha H, Chu SM. Modeling the Intensity Function of Point Process via Recurrent Neural Networkss. In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence. AAAI\u201917. AAAI Press; 2017. p. 1597\u20131603.","DOI":"10.1609\/aaai.v31i1.10724"},{"issue":"10","key":"pcbi.1009746.ref056","doi-asserted-by":"crossref","first-page":"3124","DOI":"10.1109\/TNNLS.2018.2889776","article-title":"Learning Time Series Associated Event Sequences With Recurrent Point Process Networks","volume":"30","author":"S Xiao","year":"2019","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"pcbi.1009746.ref057","article-title":"Learning Dynamic and Personalized Comorbidity Networks from Event Data using Deep Diffusion Processes","author":"Z Qian","year":"2020","journal-title":"AISTATS"},{"issue":"2","key":"pcbi.1009746.ref058","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.jamda.2019.10.022","article-title":"Adverse Outcomes of Polypharmacy in Older People: Systematic Review of Reviews","volume":"21","author":"LE Davies","year":"2020","journal-title":"Journal of the American Medical Directors Association"},{"issue":"3","key":"pcbi.1009746.ref059","first-page":"376","article-title":"Dysnatremia in Relation to Frailty and Age in Community-dwelling Adults in the National Health and Nutrition Examination Survey","volume":"72","author":"AJ Miller","year":"2017","journal-title":"Journals of Gerontology A"},{"key":"pcbi.1009746.ref060","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","article-title":"Regression models and life-tables","volume":"34","author":"DR Cox","year":"1972","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"pcbi.1009746.ref061","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1038\/s41591-019-0673-2","article-title":"Undulating changes in human plasma proteome profiles across the lifespan","volume":"25","author":"B Lehallier","year":"2019","journal-title":"Nature Medicine"},{"key":"pcbi.1009746.ref062","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1038\/s41591-019-0719-5","article-title":"Personal aging markers and ageotypes revealed by deep longitudinal profiling","volume":"26","author":"S Ahadi","year":"2020","journal-title":"Nature Medicine"},{"key":"pcbi.1009746.ref063","doi-asserted-by":"crossref","unstructured":"Cho K, van Merri\u00ebnboer B, Gulcehre C, Bahdanau D, Bougares F, Schwenk H, et al. Learning Phrase Representations using RNN Encoder\u2013Decoder for Statistical Machine Translation. In: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). Doha, Qatar: Association for Computational Linguistics; 2014. p. 1724\u20131734. Available from: https:\/\/www.aclweb.org\/anthology\/D14-1179.","DOI":"10.3115\/v1\/D14-1179"},{"issue":"3","key":"pcbi.1009746.ref064","doi-asserted-by":"crossref","first-page":"1674","DOI":"10.1016\/j.csda.2007.05.019","article-title":"Bayesian inference for nonlinear multivariate diffusion models observed with error","volume":"52","author":"A Golightly","year":"2008","journal-title":"Computational Statistics & Data Analysis"},{"issue":"2","key":"pcbi.1009746.ref065","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1214\/16-BA1009","article-title":"Bayesian Inference for Diffusion-Driven Mixed-Effects Models","volume":"12","author":"GA Whitaker","year":"2017","journal-title":"Bayesian Analysis"},{"key":"pcbi.1009746.ref066","first-page":"17","article-title":"Variational Inference for Diffusion Processes","volume":"20","author":"C Archambeau","year":"2008","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"3","key":"pcbi.1009746.ref067","doi-asserted-by":"crossref","first-page":"1800233","DOI":"10.1002\/andp.201800233","article-title":"Variational Inference for Stochastic Differential Equations","volume":"531","author":"M Opper","year":"2019","journal-title":"Annalen der Physik"},{"key":"pcbi.1009746.ref068","first-page":"1","article-title":"Scalable Gradients for Stochastic Differential Equations","volume":"118","author":"X Li","year":"2020","journal-title":"Proceedings of Machine Learning Research"},{"key":"pcbi.1009746.ref069","unstructured":"Dinh L, Sohl-Dickstein J, Bengio S. Density estimation using Real NVP. In: 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24\u201326, 2017, Conference Track Proceedings. OpenReview.net; 2017. Available from: https:\/\/openreview.net\/forum?id = HkpbnH9lx."},{"key":"pcbi.1009746.ref070","doi-asserted-by":"crossref","unstructured":"Ren K, Qin J, Zheng L, Yang Z, Zhang W, Qiu L, et al. Deep recurrent survival analysis. In: Proceedings of the AAAI Conference on Artificial Intelligence. vol. 33; 2019. p. 4798\u20134805.","DOI":"10.1609\/aaai.v33i01.33014798"},{"key":"pcbi.1009746.ref071","unstructured":"Kingma DP, Ba J. ADAM: A method for stochastic optimization. Proceedings of the 3rd International Conference on Learning Representations. 2015."},{"issue":"3","key":"pcbi.1009746.ref072","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1137\/09076636X","article-title":"Runge\u2013Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations","volume":"48","author":"A R\u00f6\u00dfler","year":"2010","journal-title":"SIAM J Numer Anal"},{"key":"pcbi.1009746.ref073","volume-title":"Springer Series in Statistics","author":"T Hastie","year":"2001"},{"key":"pcbi.1009746.ref074","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"F Pedregosa","year":"2011","journal-title":"Journal of Machine Learning Research"},{"key":"pcbi.1009746.ref075","first-page":"216","article-title":"Discussion of the paper by D. R. Cox","volume":"34","author":"NE Breslow","year":"1972","journal-title":"Journal of the Royal Statistical Society: B"},{"issue":"2","key":"pcbi.1009746.ref076","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":"H Zou","year":"2005","journal-title":"Journal of the Royal Statistical Society: B"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1009746","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T00:00:00Z","timestamp":1642723200000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009746","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T20:38:35Z","timestamp":1726432715000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009746"}},"subtitle":[],"editor":[{"given":"Tatiana","family":"Engel","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,1,10]]},"references-count":76,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1,10]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1009746","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,10]]}}}