On the application of Gaussian graphical models to paired data problems

TL;DR

This paper introduces a novel fused graphical lasso approach for Gaussian graphical models tailored to paired data, enabling the comparison of two dependent groups and their association structure, with applications in cancer genomics.

Contribution

The paper develops a fused graphical lasso method for paired Gaussian graphical models, including an ADMM algorithm and tools for penalty selection, with implementation in R.

Findings

Effective in modeling paired data with dependent groups.

Provides a comprehensive set of tools for graphical model selection.

Demonstrated application in cancer genomics comparison.

Abstract

Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointy learning their independence structures. We consider the case where there are exactly two dependent groups and the association structure is represented by a family of coloured Gaussian graphical models suited to deal with paired data problems. To learn the two dependent graphs, together with their across-graph association structure, we implement a fused graphical lasso penalty. We carry out a comprehensive analysis of this approach, with special attention to the role played by some relevant submodel classes. In this way, we provide a broad set of tools for the application of Gaussian graphical models to paired data problems. These include results useful for the specification of penalty values in order to obtain a path of lasso solutions and an ADMM algorithm that solves the fused graphical lasso optimization problem. Finally, we present an application of our method to cancer genomics where it is of interest to compare cancer cells with a control sample from histologically normal tissues adjacent to the tumor. All the methods described in this article are implemented in the $\texttt{R}$ package $\texttt{pdglasso}$ availabe at: https://github.com/savranciati/pdglasso.