{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T17:53:20Z","timestamp":1770832400797,"version":"3.50.1"},"reference-count":49,"publisher":"Oxford University Press (OUP)","issue":"18","license":[{"start":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T00:00:00Z","timestamp":1548979200000},"content-version":"vor","delay-in-days":366,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010663","name":"European Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Union\u2019s Seventh Framework Programme","award":["FP\/2007\u20132013s"],"award-info":[{"award-number":["FP\/2007\u20132013s"]}]},{"DOI":"10.13039\/100010663","name":"ERC","doi-asserted-by":"publisher","award":["617393"],"award-info":[{"award-number":["617393"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,9,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Motivation<\/jats:title><jats:p>Temporal variations in biological systems and more generally in natural sciences are typically modeled as a set of ordinary, partial or stochastic differential or difference equations. Algorithms for learning the structure and the parameters of a dynamical system are distinguished based on whether time is discrete or continuous, observations are time-series or time-course and whether the system is deterministic or stochastic, however, there is no approach able to handle the various types of dynamical systems simultaneously.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>In this paper, we present a unified approach to infer both the structure and the parameters of non-linear dynamical systems of any type under the restriction of being linear with respect to the unknown parameters. Our approach, which is named Unified Sparse Dynamics Learning (USDL), constitutes of two steps. First, an atemporal system of equations is derived through the application of the weak formulation. Then, assuming a sparse representation for the dynamical system, we show that the inference problem can be expressed as a sparse signal recovery problem, allowing the application of an extensive body of algorithms and theoretical results. Results on simulated data demonstrate the efficacy and superiority of the USDL algorithm under multiple interventions and\/or stochasticity. Additionally, USDL\u2019s accuracy significantly correlates with theoretical metrics such as the exact recovery coefficient. On real single-cell data, the proposed approach is able to induce high-confidence subgraphs of the signaling pathway.<\/jats:p><\/jats:sec><jats:sec><jats:title>Availability and implementation<\/jats:title><jats:p>Source code is available at Bioinformatics online. USDL algorithm has been also integrated in SCENERY (http:\/\/scenery.csd.uoc.gr\/); an online tool for single-cell mass cytometry analytics.<\/jats:p><\/jats:sec><jats:sec><jats:title>Supplementary information<\/jats:title><jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p><\/jats:sec>","DOI":"10.1093\/bioinformatics\/btz065","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T04:31:04Z","timestamp":1548736264000},"page":"3387-3396","source":"Crossref","is-referenced-by-count":25,"title":["A unified approach for sparse dynamical system inference from temporal measurements"],"prefix":"10.1093","volume":"35","author":[{"given":"Yannis","family":"Pantazis","sequence":"first","affiliation":[{"name":"Institute of Applied and Computational Mathematics, Foundation for Research and Technology - Hellas (FORTH) , Heraklion, Greece"}]},{"given":"Ioannis","family":"Tsamardinos","sequence":"additional","affiliation":[{"name":"Institute of Applied and Computational Mathematics, Foundation for Research and Technology - Hellas (FORTH) , Heraklion, Greece"},{"name":"Department of Computer Science, University of Crete , Heraklion, Greece"},{"name":"Gnosis Data Analysis PC , Heraklion, Greece"}]}],"member":"286","published-online":{"date-parts":[[2018,1,31]]},"reference":[{"key":"2023013108052220300_btz065-B1","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1186\/1752-0509-3-25","article-title":"Efficient, sparse biological network determination","volume":"3","author":"August","year":"2009","journal-title":"BMC Syst. Biol."},{"key":"2023013108052220300_btz065-B2","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1038\/nrg3244","article-title":"Studying and modelling dynamic biological processes using time-series gene expression data","volume":"13","author":"Bar-Joseph","year":"2012","journal-title":"Nat. Rev. Genet."},{"key":"2023013108052220300_btz065-B3","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.jtbi.2012.08.005","article-title":"A phylogenetic comparative method for studying multivariate adaptation","volume":"314","author":"Bartoszek","year":"2012","journal-title":"J. Theor. Biol."},{"key":"2023013108052220300_btz065-B4","first-page":"172","article-title":"Learning networks of stochastic differential equations","volume-title":"Advances in Neural Information Processing Systems","author":"Bento","year":"2010"},{"key":"2023013108052220300_btz065-B5","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1038\/nbt.2317","article-title":"Multiplexed mass cytometry profiling of cellular states perturbed by small-molecule regulators","volume":"30","author":"Bodenmiller","year":"2012","journal-title":"Nat. Biotechnol."},{"key":"2023013108052220300_btz065-B6","doi-asserted-by":"crossref","first-page":"2628","DOI":"10.1109\/TSP.2011.2129515","article-title":"Causal network inference via group sparse regularization","volume":"59","author":"Bolstad","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"2023013108052220300_btz065-B7","doi-asserted-by":"crossref","first-page":"R36","DOI":"10.1186\/gb-2006-7-5-r36","article-title":"The inferelator: an algorithm for learning parsimonious regulatory networks from systems-biology data sets de novo","volume":"7","author":"Bonneau","year":"2006","journal-title":"Genome Biol."},{"key":"2023013108052220300_btz065-B8","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1137\/060657704","article-title":"From sparse solutions of systems of equations to sparse modeling of signals and images","volume":"51","author":"Bruckstein","year":"2009","journal-title":"SIAM Rev."},{"key":"2023013108052220300_btz065-B9","doi-asserted-by":"crossref","first-page":"3932","DOI":"10.1073\/pnas.1517384113","article-title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems","volume":"113","author":"Brunton","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2023013108052220300_btz065-B10","doi-asserted-by":"crossref","first-page":"4680","DOI":"10.1109\/TIT.2011.2146090","article-title":"Orthogonal matching pursuit for sparse signal recovery with noise","volume":"57","author":"Cai","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2023013108052220300_btz065-B11","doi-asserted-by":"crossref","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","article-title":"Decoding by Linear Programming","volume":"51","author":"Candes","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2023013108052220300_btz065-B12","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","article-title":"Stable signal recovery from incomplete and inaccurate measurements","volume":"59","author":"Cand\u00e8s","year":"2006","journal-title":"Commun. Pure Appl. Math."},{"key":"2023013108052220300_btz065-B13","doi-asserted-by":"crossref","DOI":"10.2202\/1544-6115.1519","article-title":"Weighted-LASSO for structured network inference from time course data","volume":"9","author":"Charbonnier","year":"2010","journal-title":"Stat. Appl. Genet. Mol. Biol."},{"key":"2023013108052220300_btz065-B14","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF01404567","article-title":"Smoothing noisy data with spline functions - Estimating the correct degree of smoothing by the method of generalized cross-validation","volume":"31","author":"Craven","year":"1978","journal-title":"Numer. Math."},{"key":"2023013108052220300_btz065-B15","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1038\/ncomms9133","article-title":"Automated adaptive inference of phenomenological dynamical models","volume":"6","author":"Daniels","year":"2015","journal-title":"Nat. Commun."},{"key":"2023013108052220300_btz065-B16","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF02678430","article-title":"Adaptive greedy approximations","volume":"13","author":"Davis","year":"1997","journal-title":"Constr. Approx."},{"key":"2023013108052220300_btz065-B17","volume-title":"Numerical Methods and Modeling for Chemical Engineers","author":"Davis","year":"1984"},{"key":"2023013108052220300_btz065-B18","volume-title":"Dynamic Systems Biology Modeling and Simulation","author":"DiStefano","year":"2015"},{"key":"2023013108052220300_btz065-B19","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2023013108052220300_btz065-B20","doi-asserted-by":"crossref","first-page":"2845","DOI":"10.1109\/18.959265","article-title":"Uncertainty principles and ideal atomic decomposition","volume":"47","author":"Donoho","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2023013108052220300_btz065-B21","volume-title":"Partial Differential Equations","author":"Evans","year":"1998"},{"key":"2023013108052220300_btz065-B22","volume-title":"A Mathematical Introduction to Compressive Sensing. Applied and Numerical Harmonic Analysis","author":"Foucart","year":"2013"},{"key":"2023013108052220300_btz065-B23","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1093\/biostatistics\/kxm045","article-title":"Sparse inverse covariance estimation with the graphical lasso","volume":"9","author":"Friedman","year":"2008","journal-title":"Biostatistics"},{"key":"2023013108052220300_btz065-B24","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1016\/S1053-8119(03)00202-7","article-title":"Dynamic causal modelling","volume":"19","author":"Friston","year":"2003","journal-title":"NeuroImage"},{"key":"2023013108052220300_btz065-B25","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-05389-8","volume-title":"Handbook of Stochastic Methods: For Physics, Chemistry & the Natural Sciences","author":"Gardiner","year":"2004"},{"key":"2023013108052220300_btz065-B26","volume-title":"Stochastic Methods: A Handbook for the Natural and Social Sciences","author":"Gardiner","year":"2009"},{"key":"2023013108052220300_btz065-B27","doi-asserted-by":"crossref","first-page":"1350015","DOI":"10.1142\/S0219720013500157","article-title":"ODEion - a software module for structural identification of ordinary differential equations","volume":"12","author":"Gennemark","year":"2014","journal-title":"J. Bioinform. Comput. Biol."},{"key":"2023013108052220300_btz065-B28","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1111\/j.1749-6632.2008.03764.x","article-title":"Reverse engineering of gene networks with LASSO and nonlinear basis functions","volume":"1158","author":"Gustafsson","year":"2009","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"2023013108052220300_btz065-B29","first-page":"1157","article-title":"An Introduction to Variable and Feature Selection","volume":"3","author":"Guyon","year":"2003","journal-title":"J. Mach. Learn. Res."},{"key":"2023013108052220300_btz065-B30","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1093\/nar\/28.1.27","article-title":"KEGG: kyoto encyclopedia of genes and genomes","volume":"28","author":"Kanehisa","year":"2000","journal-title":"Nucleic Acids Res."},{"key":"2023013108052220300_btz065-B31","doi-asserted-by":"crossref","first-page":"e1005234","DOI":"10.1371\/journal.pcbi.1005234","article-title":"Sparse regression based structure learning of stochastic reaction networks from single cell snapshot time series","volume":"12","author":"Klimovskaia","year":"2016","journal-title":"PLOS Comput. Biol."},{"key":"2023013108052220300_btz065-B32","doi-asserted-by":"crossref","first-page":"1250689","DOI":"10.1126\/science.1250689","article-title":"Conditional density-based analysis of T cell signaling in single-cell data","volume":"346","author":"Krishnaswamy","year":"2014","journal-title":"Science"},{"key":"2023013108052220300_btz065-B33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-15482-4","volume-title":"Deterministic Kinetics in Chemistry and Systems Biology","author":"Lente","year":"2015"},{"key":"2023013108052220300_btz065-B34","first-page":"1","article-title":"Predictability: a problem partly solved","volume-title":"Seminar on Predictability","author":"Lorenz","year":"1996"},{"key":"2023013108052220300_btz065-B35","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/78.258082","article-title":"Matching pursuits with time-frequency dictionaries","volume":"41","author":"Mallat","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"2023013108052220300_btz065-B36","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/TMBMC.2016.2633265","article-title":"Inferring biological networks by sparse identification of nonlinear dynamics","volume":"2","author":"Mangan","year":"2016","journal-title":"IEEE Trans. Mol. Biol. Multi-Scale Commun."},{"key":"2023013108052220300_btz065-B37","first-page":"163","volume-title":"Networks: An Introduction","author":"Newman","year":"2014"},{"key":"2023013108052220300_btz065-B38","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-13050-6","volume-title":"Stochastic Differential Equations: An Introduction with Applications","author":"Oksendal","year":"1985"},{"key":"2023013108052220300_btz065-B39","doi-asserted-by":"crossref","first-page":"W270","DOI":"10.1093\/nar\/gkx448","article-title":"Scenery: a web application for (causal) network reconstruction from cytometry data","volume":"45","author":"Papoutsoglou","year":"2017","journal-title":"Nucleic Acids Res."},{"key":"2023013108052220300_btz065-B40","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/ACSSC.1993.342465","article-title":"Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition","volume-title":"Proceedings of 27th Asilomar Conference on Signals, Systems and Computers","author":"Pati","year":"1993"},{"key":"2023013108052220300_btz065-B41","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1049\/iet-syb:20060067","article-title":"Parameter estimation in ordinary differential equations for biochemical processes using the method of multiple shooting","volume":"1","author":"Peifer","year":"2007","journal-title":"IET Syst. Biol."},{"key":"2023013108052220300_btz065-B42","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1111\/j.1467-9868.2007.00610.x","article-title":"Parameter estimation for differential equations: a generalized smoothing approach","volume":"69","author":"Ramsay","year":"2007","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"2023013108052220300_btz065-B43","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1126\/science.1105809","article-title":"Causal protein-signaling networks derived from multiparameter single-cell data","volume":"308","author":"Sachs","year":"2005","journal-title":"Science"},{"key":"2023013108052220300_btz065-B44","volume-title":"An Analysis of the Finite Element Method","author":"Strang","year":"2008","edition":"2nd edn"},{"key":"2023013108052220300_btz065-B45","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":"1994","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"2023013108052220300_btz065-B46","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.1109\/TIT.2004.834793","article-title":"Greed is good: algorithmic results for sparse approximation","volume":"50","author":"Tropp","year":"2004","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2023013108052220300_btz065-B47","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1109\/TIT.2005.864420","article-title":"Just relax: convex programming methods for identifying sparse signals in noise","volume":"52","author":"Tropp","year":"2006","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2023013108052220300_btz065-B48","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal recovery from random measurements via orthogonal matching pursuit","volume":"53","author":"Tropp","year":"2007","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2023013108052220300_btz065-B49","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1186\/1752-0509-5-14","article-title":"Parameter estimation in systems biology models using spline approximation","volume":"5","author":"Zhan","year":"2011","journal-title":"BMC Syst. Biol."}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/35\/18\/3387\/48975303\/bioinformatics_35_18_3387.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/35\/18\/3387\/48975303\/bioinformatics_35_18_3387.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,14]],"date-time":"2024-07-14T11:27:52Z","timestamp":1720956472000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/35\/18\/3387\/5305020"}},"subtitle":[],"editor":[{"given":"Oliver","family":"Stegle","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2018,1,31]]},"references-count":49,"journal-issue":{"issue":"18","published-print":{"date-parts":[[2019,9,15]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btz065","relation":{},"ISSN":["1367-4803","1367-4811"],"issn-type":[{"value":"1367-4803","type":"print"},{"value":"1367-4811","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2019,9,15]]},"published":{"date-parts":[[2018,1,31]]}}}