  Undirected graphical models have many applications in such areas as machine
learning, image processing, and, recently, psychology. Psychopathology in
particular has received a lot of attention, where symptoms of disorders are
assumed to influence each other. One of the most relevant questions practically
is on which symptom (node) to intervene to have the most impact. Interventions
in undirected graphical models is equal to conditioning, and so we have
available the machinery with the Ising model to determine the best strategy to
intervene. In order to perform such calculations the partition function is
required, which is computationally difficult. Here we use a Curie-Weiss
approach to approximate the partition function in applications of
interventions. We show that when the connection weights in the graph are equal
within each clique then we obtain exactly the correct partition function. And
if the weights vary according to a sub-Gaussian distribution, then the
approximation is exponentially close to the correct one. We confirm these
results with simulations.
