Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 221 / 2 / i / a / Solution

A positive density factorizes according to an undirected graphical model $G^u=(\mathcal{V},\mathcal{E})$ when there are nonnegative clique potentials ${\psi }_C$ such thatwhere $\mathcal{C}$ may be taken as the maximal cliques and $Z$ normalizes the density. Equivalently, each potential involves only variables in one complete subgraph.