Inverse regression approach to robust nonlinear high-to-low dimensional mapping

Emeline Perthame 1 Florence Forbes 1 Antoine Deleforge 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA_D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : The goal of this paper is to address the issue of nonlinear regression with outliers, possibly in high dimension, without specifying the form of the link function and under a parametric approach. Nonlinearity is handled via an underlying mixture of affine regressions. Each regression is encoded in a joint multivariate Student distribution on the responses and covariates. This joint modeling allows the use of an inverse regression strategy to handle the high dimensionality of the data, while the heavy tail of the Student distribution limits the contamination by outlying data. The possibility to add a number of latent variables similar to factors to the model further reduces its sensitivity to noise or model misspecification. The mixture model setting has the advantage of providing a natural inference procedure using an EM algorithm. The tractability and flexibility of the algorithm are illustrated in simulations and real high-dimensional data with good performance that compares favorably with other existing methods.
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Emeline Perthame, Florence Forbes, Antoine Deleforge. Inverse regression approach to robust nonlinear high-to-low dimensional mapping. Journal of Multivariate Analysis, Elsevier, 2018, 163, pp.1 - 14. ⟨10.1016/j.jmva.2017.09.009⟩. ⟨hal-01347455v2⟩

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