Collaborative Sliced Inverse Regression

Alessandro Chiancone 1, 2, 3, 4 Stephane Girard 4, 2 Jocelyn Chanussot 3
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
3 GIPSA-SIGMAPHY - SIGMAPHY
GIPSA-DIS - Département Images et Signal, GIPSA-PSD - GIPSA Pôle Sciences des Données
Abstract : Sliced Inverse Regression (SIR) is an effective method for dimensionality reduction in high-dimensional regression problems. However, the method has requirements on the distribution of the predictors that are hard to check since they depend on unobserved variables. It has been shown that, if the distribution of the predictors is elliptical, then these requirements are satisfied. In case of mixture models, the ellipticity is violated and in addition there is no assurance of a single underlying regression model among the different components. Our approach clusterizes the predictors space to force the condition to hold on each cluster and includes a merging technique to look for different underlying models in the data. A study on simulated data as well as two real applications are provided. It appears that SIR, unsurprisingly, is not capable of dealing with a mixture of Gaussians involving different underlying models whereas our approach is able to correctly investigate the mixture.
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Alessandro Chiancone, Stephane Girard, Jocelyn Chanussot. Collaborative Sliced Inverse Regression. Communications in Statistics - Theory and Methods, Taylor & Francis, 2017, 46 (12), pp.6035--6053. ⟨10.1080/03610926.2015.1116578⟩. ⟨hal-01158061v2⟩

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