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Régression non linéaire robuste en grande dimension

Emeline Perthame 1 Florence Forbes 1 Brice Olivier 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 : Non linear regression is used to model complex relations between a target and a possibly large number of features. Nevertheless, under the common gaussian setting, outliers are known to affect the stability of the results and can lead to misleading predictions. Robust approaches that are tractable in high dimension are therefore needed 1 in order to improve the accuracy of linear or non-linear regression methods under the presence of outliers. In the proposed method, non linearity is handled via a mixture of regressions. Mixture models and paradoxically also the so-called mixture of regression models are mostly used to handle clustering issues and few articles refer to mixture models for actual prediction purposes. Interestingly, it was shown in (Deleforge et al., 2015 [1]) that a prediction approach based on mixture of regressions in a Gaussian setting was relevant. However, the method developed by these authors is not designed to perform robust regression. Therefore, we build on the work in [1] by considering mixture of Student distributions that are able to handle outliers. The parameter estimation can be performed via an EM algorithm which remains numerically feasible when the number of variables exceeds the number of observations. During the talk, intensive simulations, both on illustrative and more complex examples in high dimension, will demonstrate that the proposed model performs well in this setting. Application of the method on real datasets will also be illustrated.
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https://hal.archives-ouvertes.fr/hal-01423630
Contributor : Florence Forbes <>
Submitted on : Friday, December 30, 2016 - 5:21:10 PM
Last modification on : Thursday, May 28, 2020 - 9:16:02 PM
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Emeline Perthame, Florence Forbes, Brice Olivier, Antoine Deleforge. Régression non linéaire robuste en grande dimension. 48èmes Journées de Statistique organisées par la Société Française de Statistique, May 2016, Montpellier, France. ⟨hal-01423630⟩

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