Identification of Non-causal Graphical Models

TL;DR

This paper introduces a novel approach to estimate non-causal graphical models by formulating a covariance extension problem, resulting in autoregressive models that capture smoothing relations among variables.

Contribution

It proposes a new covariance extension framework and generalizes it to graphical ARMA models, advancing non-causal graphical model estimation methods.

Findings

Solution minimizes transportation distance with white noise process

Autoregressive non-causal graphical models are derived

Numerical experiments demonstrate effectiveness

Abstract

The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation distance with respect to white noise process is a double-sided autoregressive non-causal graphical model. Then, we generalize the paradigm to a class of graphical autoregressive moving-average models. Finally, we test the performance of the proposed method through some numerical experiments.