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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:163

Article

Perthame, Emeline¹  Forbes, Florence¹  Deleforge, Antoine² 

[1] Univ Grenoble Alpes, CNRS, Inria, LJK, F-38000 Grenoble, France

[2] Inria, Rennes, France

关键词: EM algorithm;    Inverse regression;    Mixture of regressions;    Nonlinear regression;    High dimension;    Robust regression;    Student distribution;   

DOI  :  10.1016/j.jmva.2017.09.009

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free