A Study on the Parameter Dependence of the Covariance Matrix in Gaussian Graphical Models on a One-Dimensional Chain Lattice and a Two-Dimensional Square Lattice

We investigate the parameter dependence of the covariance matrix of Gaussian graphical models (GGMs) defined on a one-dimensional chain lattice and a two-dimensional square lattice.A GGM is a multivariate Gaussian distribution defined on a graph structure, whose properties are characterized by a mean vector and a covariance matrix.The Laplacian matrices of a one-dimensional chain lattice and a two-dimensional square lattice can be diagonalized, and by exploiting this fact, we can derive the covariance matrix of a GGM.We numerically investigate the structure of the covariance matrix and clarify the parameter dependence of the covariance matrix.