Learning Inclusion-Optimal Chordal Graphs

TL;DR

This paper introduces a simple, efficient greedy algorithm for learning chordal graph structures from data, which is proven to find inclusion-optimal models under certain conditions and is validated on simulated datasets.

Contribution

It presents a novel greedy hill-climbing algorithm for learning chordal graphs that guarantees inclusion-optimality under large sample conditions.

Findings

Algorithm is proven to find inclusion-optimal structures asymptotically.

The method performs well on simulated datasets.

It offers a computationally efficient approach to structure learning.

Abstract

Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model from data. The algorithm is a greedy hill-climbing search algorithm that uses the inclusion boundary neighborhood over chordal graphs. In the limit of a large sample size and under appropriate hypotheses on the scoring criterion, we prove that the algorithm will find a structure that is inclusion-optimal when the dependency model of the data-generating distribution can be represented exactly by an undirected graph. The algorithm is evaluated on simulated datasets.