Duality for Continuous Graphical Models

TL;DR

This paper extends the duality theory for graphical models to continuous cases, specifically Gaussian models, providing an exact solution method for ladder graph structures under certain covariance conditions.

Contribution

It introduces a novel application of factor graph duality to continuous Gaussian graphical models, enabling exact solutions under specific local covariance constraints.

Findings

Exact solution method for Gaussian ladder graph models.

Efficiency depends on zero positions in local covariance matrices.

Illustrated with two toy examples.

Abstract

The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we propose a method to solve exactly the Gaussian graphical models defined on the ladder graph if certain conditions on the local covariance matrices are satisfied. Unlike the conventional approaches, the efficiency of the method depends on the position of the zeros in the local covariance matrices. The method and details of the dualization are illustrated on two toy examples.