Edge selection based on the geometry of dually flat spaces for Gaussian graphical models

Abstract

We propose a method for selecting edges in undirected Gaussian graphical models. Our algorithm takes after our previous work, an extension of Least Angle Regression (LARS), and it is based on the information geometry of dually flat spaces. Non-diagonal elements of the inverse of the covariance matrix, the concentration matrix, play an important role in edge selection. Our iterative method estimates these elements and selects covariance models simultaneously. A sequence of pairs of estimates of the concentration matrix and an independence graph is generated, whose length is the same as the number of non-diagonal elements of the matrix. In our algorithm, the next estimate of the graph is the nearest graph to the latest estimate of the concentration matrix. The next estimate of the concentration matrix is not just the projection of the latest estimate, and it is shrunk to the origin. We describe the algorithm and show results for some datasets. Furthermore, we give some remarks on model identification and prediction.