Title: Penalized latent variable models
Authors: Brice Ozenne - Copenhagen University (Denmark) [presenting]
Klaus Kahler Holst - Copenhagen University (Denmark)
Esben Budtz-Jorgensen - Copenhagen University (Denmark)
Abstract: Latent variables models (LVM) are statistical models able to relate measurements in a very flexible, and possibly complex, way. However they are not suited to study high dimensional data that arise, for instance, in genetics or in medical imaging. Moreover variable selection within LVM currently relies on stepwise testing procedures that suffer from instability. We propose to extend the Gaussian LVM to allow penalization on the mean or covariance parameters. An elastic net penalty is used for the mean parameter; this penalization includes lasso and ridge penalization as specific cases. A group lasso is used for penalizing the covariance structure. Estimation of the model relies on a proximal gradient algorithm to handle the non-derivability of the lasso penalty. The ability of the penalized LVM to identify the relevant parameters will be investigated in simulation studies including high dimensional settings. We will then assess its relevance for relating measurements of the serotonin in the human brain to the depression status of patients. The penalized LVM is implemented as an add-on of the R package lava and is available upon request.