Identification of Sparse Reciprocal Graphical Models

TL;DR

This paper introduces a new method for identifying sparse reciprocal graphical models for Gaussian stationary processes, enhancing robustness in high-order autoregressive scenarios through a regularized matrix completion approach.

Contribution

It presents a novel identification procedure leveraging reciprocal process approximation to improve robustness and computational efficiency in sparse graphical model estimation.

Findings

The method effectively handles large autoregressive orders.

It reduces the problem to eigenvalue computations of small matrices.

The approach improves robustness in model identification.

Abstract

In this paper we propose an identification procedure of a sparse graphical model associated to a Gaussian stationary stochastic process. The identification paradigm exploits the approximation of autoregressive processes through reciprocal processes in order to improve the robustness of the identification algorithm, especially when the order of the autoregressive process becomes large. We show that the proposed paradigm leads to a regularized, circulant matrix completion problem whose solution only requires computations of the eigenvalues of matrices of dimension equal to the dimension of the process.