Duality for Continuous Graphical Models
This work extends duality concepts from discrete to continuous graphical models, offering a method for exact inference in a specific graph structure, which is incremental in nature.
The paper tackles the problem of solving Gaussian graphical models on ladder graphs by applying the factor graph duality theorem to continuous models, achieving exact solutions under specific conditions on local covariance matrices.
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.