Using the chain rule, the derivative of the log partition-function in Proposition 1 is To perform the derivative, we use the identity and the fact that ∂L h ,m (θ)/∂θ h,m is nonzero for only a few h , m .
when h = 0, the marginals are given by and for h > 0, the marginals are given by where δ h,m is the Kronecker delta.