Indirect Gaussian Graph Learning beyond Gaussianity
This work addresses the challenge of graph learning for non-Gaussian data, which is an incremental improvement for statistical modeling and data analysis applications.
The paper tackles the problem of learning dependency graph structures from non-Gaussian data by proposing an iterative Gaussian graph learning algorithm that uses marginal loss functions and additive over-parametrization with shrinkage, achieving satisfactory accuracy as measured by a Bregman divergence.
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.