Stratified Gaussian Graphical Models

TL;DR

This paper introduces stratified Gaussian graphical models that incorporate context-specific independence, allowing for more flexible modeling of multivariate normal data by segmenting the space.

Contribution

It adapts the concept of context-specific independence to Gaussian graphical models, defining a new class called stratified models with tractable estimation.

Findings

Stratified models form a curved exponential family.

They enable modeling of context-specific independencies.

The models retain tractability for estimation and selection.

Abstract

Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide certain forms of context-specific independence that are natural to consider from an applied perspective. Such independencies have been earlier introduced to generalize discrete graphical models and Bayesian networks into more flexible model families. Here we adapt the idea of context-specific independence to Gaussian graphical models by introducing a stratification of the Euclidean space such that a conditional independence may hold in certain segments but be absent elsewhere. It is shown that the stratified models define a curved exponential family, which retains considerable tractability for parameter estimation and model selection.