# Learning block structured graphs in Gaussian graphical models

arXiv: https://arxiv.org/abs/2206.14274 · HTML: https://mlsanity.com/paper/2206.14274/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2022.

## Built on by (most cited first, 2 of 2)

- [Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2307.00127/) (2023)
- [Clusterpath Gaussian Graphical Modeling](https://mlsanity.com/paper/2407.00644/) (2024)

## Abstract (arXiv)

Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for block structural learning, under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single link but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional independence structure. Since the elements of a B-Spline basis have compact support, the independence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among the substances within the compound.