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Title: Supervised component-based generalized linear regression with conditionally covarying responses Authors:  Julien Gibaud - IMAG (France) [presenting]
Xavier Bry - Universite Montpellier (France)
Catherine Trottier - University of Montpellier (France)
Abstract: Originally, the Supervised Component-based Generalized Linear Regression (SCGLR) was designed to find explanatory components in a large set of possibly highly redundant covariates. This methodology optimizes a trade-off criterion between the model's Goodness-of-Fit and some Structural Relevance of directions with respect to the explanatory variables. This methodology allows both to find strong explanatory directions and to produce regularized predictors in a high-dimensional framework. Later on, SCGLR was extended with the aim to search for components in a thematic partitioning of the explanatory variables. However, SCGLR assumed the responses to be independent conditional on the explanatory covariates, which is not often realistic. To overcome this limitation, we propose to extend SCGLR by modeling the responses' conditional variance-covariance matrix using a small number of latent random variables called factors. More formally, a response matrix is assumed to depend, through a Generalized Linear Model, on a set of explanatory variables partitioned into several conceptually homogenous variable groups, viewed as explanatory themes and an unknown number of common latent factors accounting for their dependence structure. The method is tested on simulated data and then applied to a floristic ecology dataset.