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Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg
| dc.rights.license | open | en_US |
| hal.structure.identifier | Bordeaux population health [BPH] | |
| dc.contributor.author | PHILIPPS, Viviane | |
| hal.structure.identifier | Statistics In System biology and Translational Medicine [SISTM] | |
| hal.structure.identifier | Bordeaux population health [BPH] | |
| dc.contributor.author | HEJBLUM, Boris
ORCID: 0000-0003-0646-452X IDREF: 189970316 | |
| hal.structure.identifier | Statistics In System biology and Translational Medicine [SISTM] | |
| hal.structure.identifier | Bordeaux population health [BPH] | |
| dc.contributor.author | PRAGUE, Melanie | |
| hal.structure.identifier | Statistics In System biology and Translational Medicine [SISTM] | |
| hal.structure.identifier | Bordeaux population health [BPH] | |
| dc.contributor.author | COMMENGES, Daniel | |
| hal.structure.identifier | Bordeaux population health [BPH] | |
| dc.contributor.author | PROUST LIMA, Cecile
ORCID: 0000-0002-9884-955X IDREF: 114375747 | |
| dc.date.accessioned | 2021-05-07T08:39:07Z | |
| dc.date.available | 2021-05-07T08:39:07Z | |
| dc.date.created | 2020 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/27186 | |
| dc.description.abstractEn | Optimization is an essential task in many computational problems. In statistical modelling for instance, in the absence of analytical solution, maximum likelihood estimators are often retrieved using iterative optimization algorithms. R software already includes a variety of optimizers from general-purpose optimization algorithms to more specific ones. Among Newton-like methods which have good convergence properties, the Marquardt-Levenberg algorithm (MLA) provides a particularly robust algorithm for solving optimization problems. Newton-like methods generally have two major limitations: (i) convergence criteria that are a little too loose, and do not ensure convergence towards a maximum, (ii) a calculation time that is often too long, which makes them unusable in complex problems. We propose in the marqLevAlg package an efficient and general implementation of a modified MLA combined with strict convergence criteria and parallel computations. Convergence to saddle points is avoided by using the relative distance to minimum/maximum criterion (RDM) in addition to the stability of the parameters and of the objective function. RDM exploits the first and second derivatives to compute the distance to a true local maximum. The independent multiple evaluations of the objective function at each iteration used for computing either first or second derivatives are called in parallel to allow a theoretical speed up to the square of the number of parameters. We show through the estimation of 7 relatively complex statistical models how parallel implementation can largely reduce computational time. We also show through the estimation of the same model using 3 different algorithms (BFGS of optim routine, an E-M, and MLA) the superior efficiency of MLA to correctly and consistently reach the maximum. | |
| dc.description.sponsorship | Modèles Dynamiques pour les Etudes Epidémiologiques Longitudinales sur les Maladies Chroniques - ANR-18-CE36-0004 | en_US |
| dc.description.sponsorship | Biodiversité des Ecosystèmes Marins et Dynamique du Carbone dans le secteur de Kerguelen : approche intégrée - ANR-17-CE01-0013 | en_US |
| dc.language.iso | EN | en_US |
| dc.subject.en | Convergence criteria | |
| dc.subject.en | Marquardt-Levenberg | |
| dc.subject.en | Newton-Raphson | |
| dc.subject.en | Optimization | |
| dc.subject.en | Parallel computing | |
| dc.subject.en | R | |
| dc.title.en | Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg | |
| dc.type | Document de travail - Pré-publication | en_US |
| dc.subject.hal | Statistiques [stat]/Méthodologie [stat.ME] | en_US |
| dc.identifier.arxiv | 2009.03840 | en_US |
| bordeaux.hal.laboratories | Bordeaux Population Health Research Center (BPH) - U1219 | en_US |
| bordeaux.institution | Université de Bordeaux | en_US |
| bordeaux.institution | INSERM | en_US |
| bordeaux.team | SISTM_BPH | |
| bordeaux.team | BIOSTAT_BPH | |
| bordeaux.import.source | hal | |
| hal.identifier | hal-03100489 | |
| hal.version | 1 | |
| hal.export | false | |
| workflow.import.source | hal | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=PHILIPPS,%20Viviane&HEJBLUM,%20Boris&PRAGUE,%20Melanie&COMMENGES,%20Daniel&PROUST%20LIMA,%20Cecile&rft.genre=preprint |
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