Sélection de variables pour des processus ponctuels spatiaux


Speciality : Mathématiques Appliquées

15/09/2017 - 14:00 Mr Achmad Choiruddin Amphithéâtre Noël Gastinel - UFR IMAG F 022

Keywords :
  • sélecteur de Dantzig
  • lasso
  • vraisemblance de la régression logistique
  • vraisemblance de Poisson
  • Campbell theorem
  • Dantzig selector
  • logistic regression likelihood
  • Poisson likelihood
Recent applications such as forestry datasets involve the observations of spatial point pattern data combined with the observation of many spatial covariates. We consider in this thesis the problem of estimating a parametric form of the intensity function in such a context. This thesis develops feature selection procedures and gives some guarantees on their validity. In particular, we propose two different feature selection approaches: the lasso-type methods and the Dantzig selector-type procedures. For the methods considering lasso-type techniques, we derive asymptotic properties of the estimates obtained from estimating functions derived from Poisson and logistic regression likelihoods penalized by a large class of penalties. We prove that the estimates obtained from such procedures satisfy consistency, sparsity, and asymptotic normality. For the Dantzig selector part, we develop a modified version of the Dantzig selector, which we call by the adaptive linearized Dantzig selector (ALDS), to obtain the intensity estimates. More precisely, the ALDS estimates are defined as the solution to an optimization problem which minimizes the sum of coefficients of the estimates subject to linear approximation of the score vector as a constraint. We find that the estimates obtained from such methods have asymptotic properties similar to the ones proposed previously using an adaptive lasso regularization term. We investigate the computational aspects of the methods developed using either lasso-type procedures or the Dantzig selector-type approaches. We make links between spatial point processes intensity estimation and generalized linear models (GLMs), so we only have to deal with feature selection procedures for GLMs. Thus, easier computational procedures are implemented and computationally fast algorithm are proposed. Simulation experiments are conducted to highlight the finite sample performances of the estimates from each of two proposed approaches. Finally, our methods are applied to model the spatial locations a species of tree in the forest observed with a large number of environmental factors.


  • Mme Frédérique Letué (Maître de Conférénces - Université Grenoble Alpes )
  • Mr Jean François Coeurjolly (Professeur - Université du Québec à Montréal )


  • Mr Vivian Viallon (Maitre de conférences - Université Claude Bernard, Lyon )
  • Mr Jorge Mateu (Professeur - Universitat Jaume I )


  • Mme Hermine Bierme (Professeur - Université de Poitiers )
  • Mr Frédéric Lavancier (Maitre de conférences - Université de Nantes )
  • Mr Stéphane Girard (Directeur de Recherche - INRIA Grenoble Rhône-Alpes )