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

The goal of this paper is to address the issue of non linear regression with outliers possibly in high dimension, without specifying the form of the link function and under a parametric approach. Non linearity 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 modelling 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 mispecification. The mixture model setting has the advantage to provide a natural inference procedure using an EM algorithm. The tractability and flexibility of the algorithm are illustrated on real high dimensional data with good performance that compares favorably with other existing methods.