Graphical Model Gibbs distribution u over all oe[g]v: 4(o)cφ，(o,)Πp(a) v∈V e∈E is a distribution over [g] φe:[q]e→[0,1] ● each vE V independently samples XvE[g]according to ● each eEE is passed independently with probability e(Xe); X is accepted if all constraints e eE are passed.Graphical Model • Gibbs distribution µ over all σ∈[q]V : μ(σ) ∝ ∏ v∈V ϕv(σv) ∏ e∈E ϕe(σe) ϕv is a distribution over [q] ϕe : [q] e → [0,1] • each v ∈ V independently samples Xv∈[q] according to �v; • each e ∈ E is passed independently with probability �e(Xe); • X is accepted if all constraints e ∈ E are passed