Structured Mixture of linear mappings in high dimension

• Activity Number: 111 - New Dimension Reduction and Statistical Learning Methods for Biomedical Data
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Florence Forbes* and Chun-Chen Tu and Naisyin Wang and Benjamin Lemasson
• Companies: French Institute for Research in Computer Science and Automation (INRIA) and Universilty of Michigan and Universilty of Michigan and INSERM, Univ. Grenoble Alpes
• Keywords: non linear regression ; mixture of regressions ; inverse regression ; high dimension ; parsimony ; EM algorithm

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.