Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables
We address component-based regularization of a multivariate generalized linear model (GLM). A vector of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set A of additional covariates. X is partitioned into R conceptually homogenous variable groups X1,…,XR, viewed as explanatory themes. Variables in each Xr are assumed many and redundant. Thus, generalized linear regression demands dimension reduction and regularization with respect to each Xr. By contrast, variables in A are assumed few and selected so as to demand no regularization. Regularization is performed searching each Xr for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in Xr. To estimate a single-theme model, we first propose an enhanced version of Supervised Component Generalized Linear Regression (SCGLR), based on a flexible measure of structural relevance of components, and able to deal with mixed-type explanatory variables. Then, to estimate the multiple-theme model, we develop an algorithm encapsulating this enhanced SCGLR: THEME-SCGLR. The method is tested on simulated data and then applied to rainforest data in order to model the abundance of tree species.
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Subjects: | U10 - Informatique, mathématiques et statistiques, F40 - Écologie végétale, K01 - Foresterie - Considérations générales, http://aims.fao.org/aos/agrovoc/c_417, http://aims.fao.org/aos/agrovoc/c_1159, http://aims.fao.org/aos/agrovoc/c_1229, http://aims.fao.org/aos/agrovoc/c_3161, http://aims.fao.org/aos/agrovoc/c_1433, http://aims.fao.org/aos/agrovoc/c_1811, http://aims.fao.org/aos/agrovoc/c_8500, http://aims.fao.org/aos/agrovoc/c_6717, http://aims.fao.org/aos/agrovoc/c_7608, http://aims.fao.org/aos/agrovoc/c_8501, |
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dig-cirad-fr-5901402021-12-07T19:01:23Z http://agritrop.cirad.fr/590140/ http://agritrop.cirad.fr/590140/ Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables. Bry Xavier, Trottier Catherine, Mortier Frédéric, Cornu Guillaume. 2020. Statistical Modelling, 20 (1) : 96-119.https://doi.org/10.1177/1471082X18810114 <https://doi.org/10.1177/1471082X18810114> Researchers Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables Bry, Xavier Trottier, Catherine Mortier, Frédéric Cornu, Guillaume eng 2020 Statistical Modelling U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale K01 - Foresterie - Considérations générales Angola Burundi Cameroun Gabon République centrafricaine Congo République démocratique du Congo Rwanda République-Unie de Tanzanie Zambie http://aims.fao.org/aos/agrovoc/c_417 http://aims.fao.org/aos/agrovoc/c_1159 http://aims.fao.org/aos/agrovoc/c_1229 http://aims.fao.org/aos/agrovoc/c_3161 http://aims.fao.org/aos/agrovoc/c_1433 http://aims.fao.org/aos/agrovoc/c_1811 http://aims.fao.org/aos/agrovoc/c_8500 http://aims.fao.org/aos/agrovoc/c_6717 http://aims.fao.org/aos/agrovoc/c_7608 http://aims.fao.org/aos/agrovoc/c_8501 We address component-based regularization of a multivariate generalized linear model (GLM). A vector of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set A of additional covariates. X is partitioned into R conceptually homogenous variable groups X1,…,XR, viewed as explanatory themes. Variables in each Xr are assumed many and redundant. Thus, generalized linear regression demands dimension reduction and regularization with respect to each Xr. By contrast, variables in A are assumed few and selected so as to demand no regularization. Regularization is performed searching each Xr for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in Xr. To estimate a single-theme model, we first propose an enhanced version of Supervised Component Generalized Linear Regression (SCGLR), based on a flexible measure of structural relevance of components, and able to deal with mixed-type explanatory variables. Then, to estimate the multiple-theme model, we develop an algorithm encapsulating this enhanced SCGLR: THEME-SCGLR. The method is tested on simulated data and then applied to rainforest data in order to model the abundance of tree species. article info:eu-repo/semantics/article Journal Article info:eu-repo/semantics/publishedVersion http://agritrop.cirad.fr/590140/1/Bry%20et%20al.%20-%202018%20-%20Component-based%20regularization%20of%20a%20multivariate%20G.pdf text Cirad license info:eu-repo/semantics/restrictedAccess https://agritrop.cirad.fr/mention_legale.html https://doi.org/10.1177/1471082X18810114 10.1177/1471082X18810114 info:eu-repo/semantics/altIdentifier/doi/10.1177/1471082X18810114 info:eu-repo/semantics/altIdentifier/purl/https://doi.org/10.1177/1471082X18810114 |
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U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale K01 - Foresterie - Considérations générales http://aims.fao.org/aos/agrovoc/c_417 http://aims.fao.org/aos/agrovoc/c_1159 http://aims.fao.org/aos/agrovoc/c_1229 http://aims.fao.org/aos/agrovoc/c_3161 http://aims.fao.org/aos/agrovoc/c_1433 http://aims.fao.org/aos/agrovoc/c_1811 http://aims.fao.org/aos/agrovoc/c_8500 http://aims.fao.org/aos/agrovoc/c_6717 http://aims.fao.org/aos/agrovoc/c_7608 http://aims.fao.org/aos/agrovoc/c_8501 U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale K01 - Foresterie - Considérations générales http://aims.fao.org/aos/agrovoc/c_417 http://aims.fao.org/aos/agrovoc/c_1159 http://aims.fao.org/aos/agrovoc/c_1229 http://aims.fao.org/aos/agrovoc/c_3161 http://aims.fao.org/aos/agrovoc/c_1433 http://aims.fao.org/aos/agrovoc/c_1811 http://aims.fao.org/aos/agrovoc/c_8500 http://aims.fao.org/aos/agrovoc/c_6717 http://aims.fao.org/aos/agrovoc/c_7608 http://aims.fao.org/aos/agrovoc/c_8501 |
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U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale K01 - Foresterie - Considérations générales http://aims.fao.org/aos/agrovoc/c_417 http://aims.fao.org/aos/agrovoc/c_1159 http://aims.fao.org/aos/agrovoc/c_1229 http://aims.fao.org/aos/agrovoc/c_3161 http://aims.fao.org/aos/agrovoc/c_1433 http://aims.fao.org/aos/agrovoc/c_1811 http://aims.fao.org/aos/agrovoc/c_8500 http://aims.fao.org/aos/agrovoc/c_6717 http://aims.fao.org/aos/agrovoc/c_7608 http://aims.fao.org/aos/agrovoc/c_8501 U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale K01 - Foresterie - Considérations générales http://aims.fao.org/aos/agrovoc/c_417 http://aims.fao.org/aos/agrovoc/c_1159 http://aims.fao.org/aos/agrovoc/c_1229 http://aims.fao.org/aos/agrovoc/c_3161 http://aims.fao.org/aos/agrovoc/c_1433 http://aims.fao.org/aos/agrovoc/c_1811 http://aims.fao.org/aos/agrovoc/c_8500 http://aims.fao.org/aos/agrovoc/c_6717 http://aims.fao.org/aos/agrovoc/c_7608 http://aims.fao.org/aos/agrovoc/c_8501 Bry, Xavier Trottier, Catherine Mortier, Frédéric Cornu, Guillaume Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables |
description |
We address component-based regularization of a multivariate generalized linear model (GLM). A vector of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set A of additional covariates. X is partitioned into R conceptually homogenous variable groups X1,…,XR, viewed as explanatory themes. Variables in each Xr are assumed many and redundant. Thus, generalized linear regression demands dimension reduction and regularization with respect to each Xr. By contrast, variables in A are assumed few and selected so as to demand no regularization. Regularization is performed searching each Xr for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in Xr. To estimate a single-theme model, we first propose an enhanced version of Supervised Component Generalized Linear Regression (SCGLR), based on a flexible measure of structural relevance of components, and able to deal with mixed-type explanatory variables. Then, to estimate the multiple-theme model, we develop an algorithm encapsulating this enhanced SCGLR: THEME-SCGLR. The method is tested on simulated data and then applied to rainforest data in order to model the abundance of tree species. |
format |
article |
topic_facet |
U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale K01 - Foresterie - Considérations générales http://aims.fao.org/aos/agrovoc/c_417 http://aims.fao.org/aos/agrovoc/c_1159 http://aims.fao.org/aos/agrovoc/c_1229 http://aims.fao.org/aos/agrovoc/c_3161 http://aims.fao.org/aos/agrovoc/c_1433 http://aims.fao.org/aos/agrovoc/c_1811 http://aims.fao.org/aos/agrovoc/c_8500 http://aims.fao.org/aos/agrovoc/c_6717 http://aims.fao.org/aos/agrovoc/c_7608 http://aims.fao.org/aos/agrovoc/c_8501 |
author |
Bry, Xavier Trottier, Catherine Mortier, Frédéric Cornu, Guillaume |
author_facet |
Bry, Xavier Trottier, Catherine Mortier, Frédéric Cornu, Guillaume |
author_sort |
Bry, Xavier |
title |
Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables |
title_short |
Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables |
title_full |
Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables |
title_fullStr |
Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables |
title_full_unstemmed |
Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables |
title_sort |
component-based regularization of a multivariate glm with a thematic partitioning of the explanatory variables |
url |
http://agritrop.cirad.fr/590140/ http://agritrop.cirad.fr/590140/1/Bry%20et%20al.%20-%202018%20-%20Component-based%20regularization%20of%20a%20multivariate%20G.pdf |
work_keys_str_mv |
AT bryxavier componentbasedregularizationofamultivariateglmwithathematicpartitioningoftheexplanatoryvariables AT trottiercatherine componentbasedregularizationofamultivariateglmwithathematicpartitioningoftheexplanatoryvariables AT mortierfrederic componentbasedregularizationofamultivariateglmwithathematicpartitioningoftheexplanatoryvariables AT cornuguillaume componentbasedregularizationofamultivariateglmwithathematicpartitioningoftheexplanatoryvariables |
_version_ |
1758025974114418688 |