Title: The Ising distribution as a latent variable model,
Abstract: It is shown that the Ising distribution can be treated as a latent variable
model, where a set of N real-valued, correlated random variables are drawn and
used to generate N binary spins independently. This allows to approximate the
Ising distribution by a simpler model where the latent variables follow a
multivariate normal distribution, the so-called Cox distribution. The
approximation is formally related to an advanced mean field technique known as
adaptive TAP, and its domain of validity is similar. When valid, it allows a
principled replacement of the Ising distribution by a distribution much easier
to sample and manipulate.