Indirect Gaussian Graph Learning beyond Gaussianity

TL;DR

This paper introduces a novel method for learning dependency graph structures from non-Gaussian data using an additive over-parametrization approach and iterative algorithms, with proven statistical accuracy and practical effectiveness.

Contribution

It presents a new framework for Gaussian graph learning beyond Gaussian assumptions, leveraging marginal loss functions and shrinkage techniques.

Findings

Estimators achieve accurate dependency graph recovery.

Method demonstrates effectiveness on real-world data.

Statistical analysis confirms estimator reliability.

Abstract

This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive over-parametrization with shrinkage to incorporate variable dependencies into the criterion. An iterative Gaussian graph learning algorithm is proposed with ease in implementation. Statistical analysis shows that the estimators achieve satisfactory accuracy with the error measured in terms of a proper Bregman divergence. Real-life examples in different settings are given to demonstrate the efficacy of the proposed methodology.