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Tøndel, Kristin; Martens, Harald

Analyzing complex mathematical model behavior by partial least squares regression-based multivariate metamodeling. (English) Zbl 07912747

Wiley Interdiscip. Rev., WIREs Comput. Stat. 6, No. 6, 440-475 (2014).

MSC:

62-08 Computational methods for problems pertaining to statistics

Keywords:

chemometrics; computational biology; differential equations; metamodeling; multivariate analysis; nonlinear dynamics
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Full Text: DOI

References:

[1] KleijnenJPC. Design and Analysis of Simulation Experiments. 1st ed.New York: Springer; 2007.
[2] TøndelK, NiedererSA, LandS, SmithNP. Insight into model mechanisms through automatic parameter fitting: a new methodological framework for model development. BMC Syst Biol2014, 8:59.
[3] TøndelK, VikJO, MartensH, IndahlUG, SmithN, OmholtSW. Hierarchical multivariate regression‐based sensitivity analysis reveals complex parameter interaction patterns in dynamic models. Chemometr Intell Lab2013, 120:25-41. doi:10.1016/j.chemolab.2012.10.006.
[4] MartensH, VeflingstadS, PlahteE, MartensM, BertrandD, OmholtS. The genotype‐phenotype relationship in multicellular pattern‐generating models ‐ the neglected role of pattern descriptors. BMC Syst Biol2009, 3:87. doi:10.1186/1752‐0509‐3‐87.
[5] IsaevaJ, MartensM, SæbøS, WyllerJA, MartensH. The modelome of line curvature: many nonlinear models approximated by a single bi‐linear metamodel with verbal profiling. Phys Nonlinear Phenom2012, 241:877-889. doi:10.1016/j.physd.2012.02.002. · Zbl 1320.92052
[6] IsaevaJ, SæboS, WyllerJA, NhekS, MartensH. Fast and comprehensive fitting of complex mathematical models to massive amounts of empirical data. Chemometr Intell Lab2012, 117:13-21. doi:10.1016/j.chemolab.2011.04.009.
[7] IsaevaJ, SæbøS, WyllerJA, WolkenhauerO, MartensH. Nonlinear modelling of curvature by bi‐linear metamodelling. Chemometr Intell Lab2012, 117:2-12. doi:10.1016/j.chemolab.2011.04.010.
[8] TøndelK, IndahlUG, GjuvslandAB, OmholtSW, MartensH. Multi‐way metamodelling facilitates insight into the complex input‐output maps of nonlinear dynamic models. BMC Syst Biol2012, 6:88.
[9] ContiS, O’HaganA. Bayesian emulation of complex multi‐output and dynamic computer models. J Stat Plan Inference2010, 140:640-651. doi:10.1016/j.jspi.2009.08.006. · Zbl 1177.62033
[10] CacuciDG. Sensitivity and Uncertainty Analysis: Theory, vol. 1. 1st ed.Boca Raton, FL: Chapman and Hall/CRC; 2003. · Zbl 1030.60001
[11] CampbellK, McKayMD, WilliamsBJ. Sensitivity analysis when model outputs are functions. Reliab Eng Syst Saf2006, 91:1468-1472. doi:10.1016/j.ress.2005.11.049.
[12] WoldS, MartensH, WoldH. The Multivariate Calibration Method in Chemistry Solved by the Method. Lecturer Notes in Mathematics. Matrix Pencils. Heidelberg: Springer‐Verlag; 1983, 286-293.
[13] AbdiH. Partial least squares regression and projection on latent structure regression (PLS regression). WIREs: Comput Stat2010, 2:97-106. doi:10.1002/wics.51.
[14] Esposito VinziV, RussolilloG. Partial least squares algorithms and methods. WIREs: Comput Stat2013, 5:1-19. doi:10.1002/wics.1239. · Zbl 1540.62011
[15] FavoreelW, De MoorB, Van OverscheeP. Subspace state space system identification for industrial processes. J Process Control2000, 10:149-155. doi:10.1016/S0959‐1524(99)00030‐X.
[16] SobieEA. Parameter sensitivity analysis in electrophysiological models using multivariable regression. Biophys J2009, 96:1264-1274. doi:10.1016/j.bpj.2008.10.056.
[17] MartensH, MågeI, TøndelK, IsaevaJ, HøyM, SæbøS. Multi‐level binary replacement (MBR) design for computer experiments in high‐dimensional nonlinear systems. J Chemometr2010, 24:748-756.
[18] TøndelK, GjuvslandAB, MågeI, MartensH. Screening design for computer experiments: metamodelling of a deterministic mathematical model of the mammalian circadian clock. J Chemometr2010, 24:738-747.
[19] SarkarAX, SobieEA. Regression analysis for constraining free parameters in electrophysiological models of cardiac cells. PLoS Comput Biol2010, 6:9. doi:10.1371/journal.pcbi.1000914.
[20] TøndelK, IndahlUG, GjuvslandAB, VikJO, HunterP, OmholtSW, MartensH. Hierarchical cluster‐based partial least squares regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Syst Biol2011, 5:90.
[21] MansiT, VoigtI, MengueEA, IonasecR, GeorgescuB, NoackT, SeeburgerJ, ComaniciuD. Towards patient‐specific finite‐element simulation of MitralClip procedure. In: FichtingerG (ed.), MartelA (ed.), PetersT (ed.), eds. Medical Image Computing and Computer‐Assisted Intervention ‐ MICCAI 2011. Springer Berlin Heidelberg: 2011, 452-459.
[22] MansiT, GeorgescuB, HussanJ, HunterPJ, KamenA, ComaniciuD. Data‐driven reduction of a cardiac myofilament model. In: OurselinS (ed.), RueckertD (ed.), SmithN (ed.), eds. Functional Imaging and Modeling of the Heart. Berlin, Germany: Springer Berlin Heidelberg; 2013, 232-240.
[23] ZettinigO, MansiT, GeorgescuB, KayvanpourE, Sedaghat‐HamedaniF, AmrA, HaasJ, SteenH, MederB, KatusH, et al. Fast data‐driven calibration of a cardiac electrophysiology model from images and ECG. In: MoriK (ed.), SakumaI (ed.), SatoY (ed.), et al., eds. Medical Image Computing and Computer Assisted Intervention - MICCAI 2013. Berlin, Germany: Springer Berlin Heidelberg; 2013, 1-8.
[24] ZettinigO, MansiT, GeorgescuB, RapakaS, KamenA, HaasJ, FreseKS, Sedaghat‐HamedaniF, KayvanpourE, AmrA, et al. From medical images to fast computational models of heart electromechanics: an integrated framework towards clinical Use. In: OurselinS (ed.), RueckertD (ed.), SmithN (ed.), eds. Functional Imaging and Modeling of the Heart. Berlin, Germany: Springer Berlin Heidelberg; 2013, 249-258.
[25] ManfrenM, AsteN, MoshksarR. Calibration and uncertainty analysis for computer models – a meta‐model based approach for integrated building energy simulation. Appl Energy2013, 103:627-641. doi:10.1016/j.apenergy.2012.10.031.
[26] SmithNP, CrampinEJ, NiedererSA, BassingthwaighteJB, BeardDA. Computational biology of cardiac myocytes: proposed standards for the physiome. J Exp Biol2007, 210:1576-1583. doi:10.1242/jeb.000133.
[27] NiedererSA, FinkM, NobleD, SmithNP. A meta‐analysis of cardiac electrophysiology computational models. Exp Physiol2009, 94:486-495. doi:10.1113/expphysiol.2008.044610.
[28] HugheyJJ, LeeTK, CovertMW. Computational modeling of mammalian signaling networks. WIREs: Syst Biol Med2010, 2:194-209. doi:10.1002/wsbm.52.
[29] GutenkunstRN, WaterfallJJ, CaseyFP, BrownKS, MyersCR, SethnaJP. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput Biol2007, 3:e189. doi:10.1371/journal.pcbi.0030189.
[30] VilelaM, VingaS, MaiaMA, VoitEO, AlmeidaJS. Identification of neutral biochemical network models from time series data. BMC Syst Biol2009, 3:47. doi:10.1186/1752‐0509‐3‐47.
[31] CacuciDG, Ionescu‐BujorM, NavonIM. Sensitivity and Uncertainty Analysis: Applications to Large‐Scale Systems, vol. 2. 1st ed.Boca Raton, FL: CRC Press; 2005. · Zbl 1083.60002
[32] SaltelliA, RattoM, AndresT, CampolongoF, CariboniJ, GatelliD, SaisanaM, TarantolaS. Global Sensitivity Analysis. The Primer. Chichester, UK: Wiley‐Interscience; 2008. · Zbl 1161.00304
[33] LloydCM, LawsonJR, HunterPJ, NielsenPF. The CellML model repository. Bioinformatics2008, 24:2122-2123. doi:10.1093/bioinformatics/btn390.
[34] FennerJ, BrookB, ClapworthyG, CoveneyP, FeipelV, GregersenH, HoseD, KohlP, LawfordP, McCormackK, et al. The EuroPhysiome, STEP and a roadmap for the virtual physiological human. Philos Trans R Soc Math Phys Eng Sci2008, 366:2979-2999. doi:10.1098/rsta.2008.0089.
[35] ClapworthyG, VicecontiM, CoveneyPV, KohlP. The virtual physiological human: building a framework for computational biomedicine I. Editorial. Philos Transact A Math Phys Eng Sci2008, 366:2975-2978. doi:10.1098/rsta.2008.0103.
[36] HunterP, CoveneyPV, deBonoB, DiazV, FennerJ, FrangiAF, HarrisP, HoseR, KohlP, LawfordP, et al. A vision and strategy for the virtual physiological human in 2010 and beyond. Philos Trans R Soc Math Phys Eng Sci2010, 368:2595-2614. doi:10.1098/rsta.2010.0048.
[37] HuckaM, FinneyA, SauroHM, BolouriH, DoyleJC, KitanoH, ArkinAP, BornsteinBJ, BrayD, Cornish‐BowdenA, et al. The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics2003, 19:524-531. doi:10.1093/bioinformatics/btg015.
[38] HunterPJ, BorgTK. Integration from proteins to organs: the physiome project. Nat Rev Mol Cell Biol2003, 4:237-243. doi:10.1038/nrm1017.
[39] CrampinEJ, HalsteadM, HunterP, NielsenP, NobleD, SmithN, TawhaiM. Computational physiology and the Physiome Project. Exp Physiol2004, 89:1-26.
[40] BassingthwaighteJ, HunterP, NobleD. The cardiac physiome: perspectives for the future. Exp Physiol2009, 94:597-605. doi:10.1113/expphysiol.2008.044099.
[41] HunterP. Modeling Human Physiology: The IUPS/EMBS Physiome Project. 2010. Available at: http://researchspace.auckland.ac.nz/handle/2292/239. (Accessed August 18, 2010).
[42] KohlP, CoveneyP, ClapworthyG, VicecontiM. The virtual physiological human. Editorial. Philos Transact A Math Phys Eng Sci2008, 366:3223-3224. doi:10.1098/rsta.2008.0102.
[43] KohlP, NobleD. Systems biology and the virtual physiological human. Mol Syst Biol2009, 5:292. doi:10.1038/msb.2009.51.
[44] KohlP, VicecontiM. The virtual physiological human: computer simulation for integrative biomedicine II. Philos Transact A Math Phys Eng Sci2010, 368:2837-2839. doi:10.1098/rsta.2010.0098.
[45] LawfordPV, NarracottAV, McCormackK, BisbalJ, MartinC, BrookB, ZachariouM, KohlP, FletcherK, Diaz‐ZuccariniV. Virtual physiological human: training challenges. Philos Trans R Soc Math Phys Eng Sci2010, 368:2841-2851. doi:10.1098/rsta.2010.0082.
[46] NiedererSA, KerfootE, BensonAP, BernabeuMO, BernusO, BradleyC, CherryEM, ClaytonR, FentonFH, GarnyA, et al. Verification of cardiac tissue electrophysiology simulators using an N‐version benchmark. Philos Trans R Soc Math Phys Eng Sci2011, 369:4331-4351. doi:10.1098/rsta.2011.0139.
[47] FriedmanLW. The Simulation Metamodel. Norwell, MA: Kluwer Academic Publishers; 1996.
[48] EmmerichM, GiotisA, ÖzdemirM, BäckT, GiannakoglouK. Metamodel‐Assisted Evolution Strategies. In: Parallel Problem Solving from Nature, vol. VII. Berlin, Germany: Springer; 2002, 361-370.
[49] MeckesheimerM, BookerAJ, BartonRR, SimpsonTW. Computationally inexpensive metamodel assessment strategies. AIAA J2002, 40:2053-2060.
[50] TuJ. Cross‐validated multivariate metamodeling methods for physics‐based computer simulations. In: Proceedings of the IMAC‐XXI, Kissimmee, Florida, 2003.
[51] HendrickxW, DhaeneT. In: The Fourth International Workshop on Multidimensional Systems ‐ NDS, Wuppertal, Germany, 2005, 212-216.
[52] VianaFAC, GoguC, HaftkaRT. Making the most out of surrogate models: tricks of the trade. In: ASME 2010 International Design Engineering Technical Conference IDETC/CIE, Montreal, Canada, 2010.
[53] BoopathyK, RumpfkeilMP. A multivariate interpolation and regression enhanced kriging surrogate model. In: 21st AIAA Fluid Dynamics Conference, San Diego, USA, 2013.
[54] ShihDT, KimSB, ChenVCP, RosenbergerJM, PillaVL. Efficient computer experiment‐based optimization through variable selection. Ann Oper Res2014, 216:287-305. doi:10.1007/s10479‐012‐1129‐y. · Zbl 1296.90083
[55] BatmazI, TunaliS. Small response surface designs for metamodel estimation. Eur J Oper Res2003, 145:455-470. · Zbl 1011.90506
[56] KalosMH, WhitlockPA. Monte Carlo Methods Volume 1: Basics. 1st ed.New York: John Wiley & Sons, Inc.; 1986. · Zbl 0655.65004
[57] LiuJS. Monte Carlo Strategies in Scientific Computing. New York: Springer; 2008. · Zbl 1132.65003
[58] SantnerTJ, WilliamsBJ, NotzW. The Design and Analysis of Computer Experiments. New York: Springer; 2003. · Zbl 1041.62068
[59] McKayMD, LosASL, BeckmanRJ, ConoverWJ. Comparison the three methods for selecting values of input variable in the analysis of output from a computer code. Technometrics1979, 21:239-245. · Zbl 0415.62011
[60] MartensH. Non‐linear multivariate dynamics modelled by PLSR. In: 6th International Conference on Partial Least Squares and Related Methods. Publishing House of Electronics Industry, Beijing, 2009, 139-144.
[61] MartensH, TøndelK, TafintsevaV, KohlerA, PlahteE, VikJO, GjuvslandAB, OmholtSW. ‐based multivariate metamodeling of dynamic systems. In: AbdiH (ed.), ChinWW (ed.), VinziVE (ed.), et al., eds. New Perspectives in Partial Least Squares and Related Methods. New York: Springer; 2013, 3-30.
[62] AllenTT, YuL, SchmitzJ. An experimental design criterion for minimizing meta‐model prediction errors applied to die casting process design. J R Stat Soc Ser C Appl Stat2003, 52:103-117. · Zbl 1111.62385
[63] WangH, LiE, LiGY, ZhongZH. Development of metamodeling based optimization system for high nonlinear engineering problems. Adv Eng Softw2008, 39:629-645. doi:10.1016/j.advengsoft.2007.10.001.
[64] XiongF, XiongY, ChenW, YangS. Optimizing Latin hypercube design for sequential sampling of computer experiments. Eng Optim2009, 41:793-810. doi:10.1080/03052150902852999.
[65] MartensH, StarkE. Extended multiplicative signal correction and spectral interference subtraction: new preprocessing methods for near infrared spectroscopy. J Pharm Biomed Anal1991, 9:625-635.
[66] KohlerA, Sulé‐SusoJ, SockalingumGD, TobinM, BahramiF, YangY, PijankaJ, DumasP, CotteM, van PittiusDG, et al. Estimating and correcting Mie scattering in synchrotron‐based microscopic fourier transform infrared spectra by extended multiplicative signal correction. Appl Spectrosc2008, 62:259-266. doi:10.1366/000370208783759669.
[67] KohlerA, ZimonjaM, SegtnanV, MartensH. Normal variate, multiplicative signal correction and extended multiplicative signal correction preprocessing in biospectroscopy. In: BrownS (ed.), TaulerR (ed.), WalczB (ed.), eds. Comprehensive Chemometrics. Oxford: Elsevier; 2009, 139-162.
[68] MartensH, NæsT. Multivariate Calibration. Chichester: John Wiley and Sons; 1989. · Zbl 0732.62109
[69] WoldS, RuheA, WoldH, DunnWJ. The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses. SIAM J Sci Stat Comput1984, 5:735-743. · Zbl 0545.62044
[70] MartensH, MartensM. NIR spectroscopy ‐ applied philosophy. Infra‐red spectroscopy. In: HildrumKI (ed.), IsakssonT (ed.), NaesT (ed.), TandbergA (ed.), eds. Bridging Gap Data Analisis and NIR Applications. Chichester: Ellis Horwood; 1992, 1-10.
[71] MartensH, MartensM. Multivariate Analysis of Quality: An Introduction. 1st ed.Chichester: John Wiley & Sons Ltd.; 2001.
[72] MartensH. The informative converse paradox: windows into the unknown. Chemometr Intell Lab2011, 107:124-138. doi:16/j.chemolab.2011.02.007.
[73] MalinowskiK, McAvoyTJ, GeorgeR, DieterichS, D’SouzaWD. Maintaining tumor targeting accuracy in real‐time motion compensation systems for respiration‐induced tumor motion. Med Phys2013, 40:071709. doi:10.1118/1.4808119.
[74] VikJO, GjuvslandAB, LiL, TøndelK, NiedererSA, SmithN, HunterPJ, OmholtSW. Genotype‐phenotype map characteristics of an in silico heart cell. Front Genomic Physiol2011, 2:106. doi:10.3389/fphys.2011.00106.
[75] TafintsevaV, TøndelK, PonosovA, MartensH. Global structure of sloppiness in a nonlinear model. J Chemometr2014, doi:10.1002/cem.2651.
[76] WalczakB, MassartDL. Local modelling with radial basis function networks. Chemometr Intell Lab2000, 50:179-198. doi:10.1016/S0169‐7439(99)00056‐8.
[77] CzekajT, WuW, WalczakB. About kernel latent variable approaches and SVM. J Chemometr2005, 19:341-354. doi:10.1002/cem.937.
[78] ZerzuchaP, DaszykowskiM, WalczakB. Dissimilarity partial least squares applied to non‐linear modeling problems. Chemometr Intell Lab2012, 110:156-162. doi:10.1016/j.chemolab.2011.11.005.
[79] ZerzuchaP, WalczakB. Concept of (dis)similarity in data analysis. TrAC Trends Anal Chem2012, 38:116-128. doi:10.1016/j.trac.2012.05.005.
[80] BroR. PARAFAC. Tutorial and applications. Chemometr Intell Lab1997, 38:149-171. doi:16/S0169‐7439(97)00032‐4.
[81] BroR. Multiway calibration. Multilinear PLS. J Chemometr1996, 10:47-61. doi:10.1002/(SICI)1099‐128X(199601)10:1<47::AID‐CEM400>3.0.CO;2‐C.
[82] NordbøØ. Constructing and exploring the parameter‐to‐phenotype map of the passively inflated ventricle. PhD Thesis, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 2013.
[83] MartensHA, DardenneP. Validation and verification of regression in small data sets. Chemometr Intell Lab1998, 44:99-121. doi:10.1016/S0169‐7439(98)00167‐1.
[84] WuT, MartensH, HunterP, MithraratneK. Emulating facial biomechanics using multivariate partial least squares surrogate models. Int J Numer Methods Biomed Eng2014, doi:10.1002/cnm.2646.
[85] WuT, MartensH, HunterP, MithraratneK. Estimating muscle activation patterns using a surrogate model of facial biomechanics. In: 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Osaka, Japan, 2013, 7172-7175.
[86] ChuiliS, HahnJ (2005) On the use of partial least squares () and balancing for nonlinear model reduction. IEEE, 2572-2577.
[87] GubskayaAV, KholodovychV, KnightD, KohnJ, WelshWJ. Prediction of fibrinogen adsorption for biodegradable polymers: integration of molecular dynamics and surrogate modeling. Polymer2007, 48:5788-5801. doi:10.1016/j.polymer.2007.07.007.
[88] WeiZ, WeiW, GuofengX. Non‐Linear Partial Least Squares Response Surface Method for Structural Reliability Analysis. Harbin, China: Harbin Institute of Technology, HIT; 2012.
[89] GauchiJ‐P. PLS‐based global sensitivity analysis for numerical models. An application to aircraft infrared signatures. In: The 7th International Conference on Partial Least Squares and Related Methods. Houston, TX: Springer Verlag; 2012, 1-7.
[90] TøndelK. Prediction of homology model quality with multivariate regression. J Chem Inf Comput Sci2004, 44:1540-1551. doi:10.1021/ci049924m.
[91] LehutaS, MahévasS, PetitgasP, PelletierD. Combining sensitivity and uncertainty analysis to evaluate the impact of management measures with ISIS-fish: marine protected areas for the Bay of Biscay anchovy (Engraulis encrasicolus) fishery. ICES J Mar Sci2010, 67:1063-1075. doi:10.1093/icesjms/fsq002.
[92] MartensM, VeflingstadSR, PlahteE, BertrandD, MartensH. A sensory scientific approach to visual pattern recognition of complex biological systems. Food Qual Prefer2010, 21:977-986. doi:10.1016/j.foodqual.2010.04.013.
[93] BerglundA, WoldS. INLR, implicit non‐linear latent variable regression. J Chemometr1997, 11:141-156. doi:10.1002/(SICI)1099‐128X(199703)11:2<141::AID‐CEM461>3.0.CO;2‐2.
[94] WestadF, DiepoldK, MartensH. QR‐PLSR: Reduced‐rank regression for high‐speed hardware implementation. J Chemometr1996, 10:439-451. doi:10.1002/(SICI)1099‐128X(199609)10:5/6<439::AID‐CEM443>3.0.CO;2‐C.
[95] SrinivasanBV, SchwartzWR, DuraiswamiR, DavisL Partial least squares on graphical processor for efficient pattern recognition. Computer Science Department, University of Maryland; CS‐TR‐4968, 2010.
[96] HassaniS, MartensH, QannariEM, HanafiM, BorgeGI, KohlerA. Analysis of ‐ omics data: graphical interpretation ‐ and validation tools in multi‐block methods. Chemometr Intell Lab2010, 104:140-153. doi:10.1016/j.chemolab.2010.08.008.
[97] NæsT, TomicO, MevikB‐H, MartensH. Path modelling by sequential PLS regression. J Chemometr2011, 25:28-40. doi:10.1002/cem.1357.
[98] AbdiH, WilliamsLJ. Partial least squares methods: partial least squares correlation and partial least square regression. Methods Mol Biol2013, 930:549-579. doi:10.1007/978‐1‐62703‐059‐5_23.
[99] KlompstraMB, BakkerGJ, BlomHAP. Sensitivity analysis in Monte Carlo simulation based rare event estimation. Safety, Complexity and Responsibility based design and validation of highly automated Air Traffic Management; EU project no. TREN/07/FP6AE/S07.71574/037180 IFLY Deliverable D7.2f, Version 1.3, 2010.
[100] De JongS. SIMPLS: An alternative approach to partial least squares regression. Chemometr Intell Lab1993, 18:251-263. doi:10.1016/0169‐7439(93)85002‐X.
[101] AnderssonM. A comparison of nine PLS1 algorithms. J Chemometr2009, 23:518-529. doi:10.1002/cem.1248.
[102] GolubG, KahanW. Calculating the singular values and pseudo‐inverse of a matrix. J Soc Ind Appl Math Ser B Numer Anal1965, 2:205-224. · Zbl 0194.18201
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