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Supervised Component Generalized Linear Regression with Multiple Explanatory Blocks: THEME-SCGLR

  • Xavier BryEmail author
  • Catherine Trottier
  • Fréderic Mortier
  • Guillaume Cornu
  • Thomas Verron
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 173)

Abstract

We address component-based regularization of a multivariate Generalized Linear Model (GLM). A set of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set T of additional covariates. X is partitioned into R conceptually homogeneous blocks X1, , X R , viewed as explanatory themes. Variables in each X r are assumed many and redundant. Thus, generalized linear regression demands regularization with respect to each X r . By contrast, variables in T are assumed selected so as to demand no regularization. Regularization is performed searching each X r for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X r . We propose a very general criterion to measure structural relevance (SR) of a component in a block, and show how to take SR into account within a Fisher-scoring-type algorithm in order to estimate the model. We show how to deal with mixed-type explanatory variables. The method, named THEME-SCGLR, is tested on simulated data, and then applied to rainforest data in order to model the abundance of tree-species.

Keywords

Component-based regularization Generalized linear model (GLM) Regularization 

Notes

Acknowledgements

This research was supported by the CoForChange project (http://www.coforchange.eu/) funded by the ERA-Net BiodivERsA with the national funders ANR (France) and NERC (UK), part of the 2008 BiodivERsA call for research proposals involving 16 European, African and international partners including a number of timber companies (see the list on the website, http://www.coforchange.eu/partners), and by the CoForTips project funded by the ERA-Net BiodivERsA with the national funders FWF (Austria), BelSPO (Belgium) and ANR (France), part of the 2011–2012 BiodivERsA call for research proposals (http://www.biodiversa.org/519).

References

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Xavier Bry
    • 1
    Email author
  • Catherine Trottier
    • 2
  • Fréderic Mortier
    • 3
  • Guillaume Cornu
    • 3
  • Thomas Verron
    • 4
  1. 1.Institut Montpelliérain Alexander Grothendieck, UM2, Place Eugène BataillonMontpellierFrance
  2. 2.Université Montpellier 3MontpellierFrance
  3. 3.Cirad – UR Biens et Services des Ecosystèmes Forestiers tropicaux – – 34398 MontpellierMontpellierFrance
  4. 4.ITG-SEITA – Centre de recherche SCR – 4 rue André Dessaux – 45404Fleury-les-AubraisFrance

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