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Structured Mixture of linear mappings in high dimension

Chun-Chen Tu 1 Florence Forbes 2 Naisyin Wang 3 Benjamin Lemasson 4 
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : We address the issue of non linear regression in high dimension. Non linearity is handled via an underlying mixture of affine regressions. Each regression is encoded in a joint multivariate Gaussian 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. The mixture model setting provides a natural inference procedure using an EM algorithm. However, since the clustering is conducted at the combined high dimension of both responses and covariates, the distance between two members of the same cluster (mixture component) in the response space could still remain large. As a result, a mixture component can contain several sub-clusters violating the model's Gaussian assumption with a potential severe impact on prediction performance. A way to counteract this effect is to increase the number of components but at the cost of an increased number of parameters. We therefore propose a parsimonious approach referred to as Structured Mixture of Gaussian Locally Linear Mapping to solve the aforementioned problems. The performance is illustrated on simulated and real high dimensional data.
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Submitted on : Friday, December 1, 2017 - 4:00:42 PM
Last modification on : Friday, November 18, 2022 - 9:25:33 AM


  • HAL Id : hal-01653601, version 1



Chun-Chen Tu, Florence Forbes, Naisyin Wang, Benjamin Lemasson. Structured Mixture of linear mappings in high dimension. JSM 2017 - Joint Statistical Meeting, Jul 2017, Baltimore, United States. ⟨hal-01653601⟩



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