A coherent framework for learning spatiotemporal piecewise- geodesic trajectories from longitudinal manifold-valued data
| Autor: | Chevallier, Juliette, Debavelaere, Vianney, Allassonnière, Stéphanie |
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| Přispěvatelé: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche des Cordeliers (CRC), Université Paris Diderot - Paris 7 (UPD7)-École pratique des hautes études (EPHE)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM), Ce travail bénéficie d'un financement public Investissement d'avenir, réference ANR-11-LABX-0056-LMH. This work was supported by a public grant as part of the Investissement d'avenir, project reference ANR-11-LABX-0056-LMH., Travail réalisé dans le cadre d'un projet financé par la Fondation de la Recherche Médicale, 'DBI20131228564'. Work performed as a part of a project funded by the Fondation of Medical Research, grant number 'DBI20131228564'., Department of Medical Oncology, Hôpital Européen Georges Pompidou [APHP] (HEGP), Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO)-Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO), Centre de Mathématiques Appliquées - Ecole Polytechnique ( CMAP ), École polytechnique ( X ) -Centre National de la Recherche Scientifique ( CNRS ), Hôpital Européen Georges Pompidou [APHP] ( HEGP ), Centre de Recherche des Cordeliers ( CRC ), Université Paris Diderot - Paris 7 ( UPD7 ) -École pratique des hautes études ( EPHE ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
[ MATH ] Mathematics [math]
[ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation [STAT.AP]Statistics [stat]/Applications [stat.AP] Longitudinal data Bayesian estimation Spatio-temporal analysis [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation MCMC methods [ STAT.ME ] Statistics [stat]/Methodology [stat.ME] [STAT.ML]Statistics [stat]/Machine Learning [stat.ML] [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] EM like algorithm [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST] [MATH]Mathematics [math] [STAT.ME]Statistics [stat]/Methodology [stat.ME] Nonlinear mixed-effects model |
| Popis: | This paper provides a coherent framework for studying longitudinal manifold-valued data. We introduce a Bayesian mixed-effects model which allows to estimate both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and inter-individual variability. We prove the existence of the maximum a posteriori estimate and its asymptotic consistency under reasonable assumptions. Due to the non-linearity of the proposed model, we use a stochastic version of Expectation-Maximization algorithm to estimate the model parameters. Our simulations show that our model is not noise-sensitive and succeed in explaining various paths of progression. |
| Databáze: | OpenAIRE |
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