Generalized Stability Approach for Regularized Graphical Models

TL;DR

This paper enhances the Stability Approach to Regularization Selection (StARS) for graphical models by introducing computationally efficient bounds and extending stability criteria to subgraphs, improving graph recovery performance.

Contribution

It provides computationally efficient bounds for StARS and generalizes the stability criterion from edges to subgraphs, advancing high-dimensional graphical model selection.

Findings

Reduced computational cost for graph selection.

Improved graph recovery performance.

Stable selection of regularization parameters.

Abstract

Selecting regularization parameters in penalized high-dimensional graphical models in a principled, data-driven, and computationally efficient manner continues to be one of the key challenges in high-dimensional statistics. We present substantial computational gains and conceptual generalizations of the Stability Approach to Regularization Selection (StARS), a state-of-the-art graphical model selection scheme. Using properties of the Poisson-Binomial distribution and convex non-asymptotic distributional modeling we propose lower and upper bounds on the StARS graph regularization path which results in greatly reduced computational cost without compromising regularization selection. We also generalize the StARS criterion from single edge to induced subgraph (graphlet) stability. We show that simultaneously requiring edge and graphlet stability leads to superior graph recovery performance independent of graph topology. These novel insights render Gaussian graphical model selection a routine task on standard multi-core computers.