Information-geometry-driven graph sequential growth

TL;DR

This paper introduces a novel, regularisation-free method for Gaussian graphical inference using information-geometry-driven sequential graph growth, which effectively identifies sparse models with minimal false detections.

Contribution

It proposes a new approach linking graph growth to coordinate descent, enabling efficient, tuning-parameter-free inference of sparse Gaussian graphical models.

Findings

Reliable extraction of sparse graphical models

Limited false detections in inferred graphs

Activation ranks reveal edge relevance

Abstract

We investigate the properties of a class of regularisation-free approaches for Gaussian graphical inference based on the information-geometry-driven sequential growth of initially edgeless graphs. Relating the growth of a graph to a coordinate descent process, we characterise the fully-corrective descents corresponding to information-optimal growths, and propose numerically efficient strategies for their approximation. We demonstrate the ability of the proposed procedures to reliably extract sparse graphical models while limiting the number of false detections, and illustrate how activation ranks can provide insight into the informational relevance of edge sets. The considered approaches are tuning-parameter-free and have complexities akin to coordinate descents.