Marginalizing in Undirected Graph and Hypergraph Models
This work addresses a theoretical problem in probabilistic graphical modeling, offering incremental improvements for researchers in statistics and machine learning.
The paper tackles the problem of marginalizing in undirected graph and hypergraph models by introducing operators to derive marginal distributions that factorize appropriately, showing that hypergraph models enable finer factorization and more precise conditional independence analysis than graph models.
Given an undirected graph G or hypergraph X model for a given set of variables V, we introduce two marginalization operators for obtaining the undirected graph GA or hypergraph HA associated with a given subset A c V such that the marginal distribution of A factorizes according to GA or HA, respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that hypergraph models allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models.