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Séminaire
Séminaire d'unité
Nom intervenant
Bastien Batardière & Jérémy Lamourroux
Résumé
 

Bastien Batardière

 

Title: Finite-sum optimization: adaptivity to smoothness and loopless variance reduction
 
Abstract: For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past gradients and thereby adapt to the geometry of the objective function. Variants such as RMSprop and Adam demonstrate outstanding practical performance that have contributed to the success of deep learning. In this work, we present AdaVR, which combines the AdaGrad algorithm with variance-reduced gradient estimators such as SAGA or L-SVRG. We assess that AdaVR inherits both good convergence properties from VR methods and the adaptive nature of AdaGrad: in the case of $L$-smooth convex functions we establish a gradient complexity of $O(n+(L+\sqrt{nL})/\varepsilon)$ without prior knowledge of $L$. Numerical experiments demonstrate the superiority of AdaVR over state-of-the-art methods. Moreover, we empirically show that the RMSprop and Adam algorithm combined with variance-reduced gradients estimators achieve even faster convergence.
 
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Jérémy Lamouroux

 

Titre : Influence of contextual elements on the spatial modelling of atmospheric cadmium accumulated by mosses


Bio : Doctorant en deuxième année de l'école doctorale de mathématiques Jacques Hadamard (EDMH), je réalise une thèse sous l'encadrement d'Isabelle Albert (INRAE) et co-encadrée par Sébastien Leblond et Caroline Meyer du Muséum National d'Histoire Naturelle (MNHN). Je suis rattaché à l'UMR de Mathématique et Informatique Appliquées d'AgroParisTech-INRAE (MIA-Paris Saclay).


Abstract : Since the 1960s, terrestrial mosses have been used for monitoring studies of trace element deposits. The BRAMM network monitors these elements in rural areas, under tree cover, using monospecific moss samples evenly spread across the territory. Investigating metal accumulation in mosses with contextual elements provides valuable insights for policymakers. This study focuses on regional cadmium (observed Cd ϵ [0.03;1.16] μg/g) deposition and the production of spatial distribution maps. We compare Cd accumulation with several contextual elements in 445 French forested sites separated according to bioclimatic zones. Contextual elements used are the concentration of the cd in the atmosphere and cd deposition modelled by the European Monitoring and Evaluation Programme (EMEP), type of moss sampling, type of forest cover, road distance, and land use defined by Corine Land Cover. This gives us a total of 60 covariates. The aim is to produce spatial models in which coefficients relating concentration in mosses and contextual elements will vary from one territory to another. We use linear models if no spatial effects are present in the area. Otherwise, we enhance the linear model by incorporating spatial random effects using the INLA package in R, which modelises Stochastic Partial Differential Equations (SPDE), which considers spatial correlation.

Lieu
Salle E.1.505
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Date de fin du Workshop