On the Equivalence of Gaussian Graphical Models Defined on Complete Bipartite Graphs
Journal:
arXiv
Published Date:
May 5, 2025
Abstract
This paper introduces two Gaussian graphical models defined on complete
bipartite graphs. We show that the determinants of the precision matrices
associated with the models are equal up to scale, where the scale factor only
depends on model parameters. In this context, we will introduce a notion of
``equivalence" between the two Gaussian graphical models. This equivalence has
two key applications: first, it can significantly reduce the complexity of
computing the exact value of the determinant, and second, it enables the
derivation of closed-form expressions for the determinants in certain special
cases.
