We show 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 resulting approximation bears similarities with the Thouless Anderson Palmer (TAP) solution from mean field theory, but retains a broader range of applicability when the coupling weights are not independently distributed. Moreover, unlike classic mean field approaches, the approximation can be used to generate correlated spin patterns .
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 .
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We show
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. The resulting approximation bears similarities with the Thouless Anderson Palmer (TAP) solution from mean field theory, but retains a broader range of applicability when the coupling weights are not independently distributed. Moreover, unlike classic mean field approaches, the approximation can be used to generate correlated spin patterns
, 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