Standard imsets for undirected and chain graphical models

TL;DR

This paper introduces standard imsets for undirected and chain graphical models, utilizing triangulations of graphs to generalize and describe their structures in a unified framework.

Contribution

It provides a novel method to derive standard imsets for both undirected and chain graphical models through triangulation techniques.

Findings

Standard imsets for undirected graphs are based on minimal triangulations.

Triangulation of chain graphs enables generalization of imsets.

The approach unifies the representation of different graphical models.

Abstract

We derive standard imsets for undirected graphical models and chain graphical models. Standard imsets for undirected graphical models are described in terms of minimal triangulations for maximal prime subgraphs of the undirected graphs. For describing standard imsets for chain graphical models, we first define a triangulation of a chain graph. We then use the triangulation to generalize our results for the undirected graphs to chain graphs.