Graphical Models for Multivariate Count Data

What the math gives to ML

The paper provides graph-supported count distributions whose support and dependence structure are controlled by a decomposable graph, with explicit sampling and Bayesian posterior and predictive updates. The transferable asset is the ability to make a neural output distribution obey hard incompatibility constraints while retaining a normalized likelihood and graph-local factorization. A practical adaptation is a graph-constrained categorical or routing head in which neural logits define weights over independent sets and inference uses exact junction-tree variable elimination for low-treewidth graphs. This is useful when outputs must satisfy exclusion constraints, such as selecting mutually incompatible experts, graph actions, entities, or simultaneously active labels.