Inference of Multiscale Gaussian Graphical Model
This addresses the need for stable GGM estimation in fields like genomics and ecology, but it appears incremental as it builds on existing lasso-based methods.
The paper tackled the problem of estimating Gaussian Graphical Models (GGMs) in high-dimensional settings where variable clustering is needed, by proposing a method that simultaneously infers hierarchical clustering and independence graphs at each level, with results demonstrated on real and synthetic data.
Gaussian Graphical Models (GGMs) are widely used for exploratory data analysis in various fields such as genomics, ecology, psychometry. In a high-dimensional setting, when the number of variables exceeds the number of observations by several orders of magnitude, the estimation of GGM is a difficult and unstable optimization problem. Clustering of variables or variable selection is often performed prior to GGM estimation. We propose a new method allowing to simultaneously infer a hierarchical clustering structure and the graphs describing the structure of independence at each level of the hierarchy. This method is based on solving a convex optimization problem combining a graphical lasso penalty with a fused type lasso penalty. Results on real and synthetic data are presented.