Graphical Model ●Gibbs distribution u over all o∈[q]': a(o)cΠ,(a,)Πg e(ou,O) G(V,E) v∈V e=(u,v)∈E Ising/Potts model: (ferromagnetic) if ou=oy or了 10.1 otherwise (anti-ferromagnetic) a,ow={eolee otherwise is a distribution over [g]( (arbitrary local fields)Graphical Model • Gibbs distribution µ over all σ∈[q]V : μ(σ) ∝ ∏ v∈V ϕv(σv) ∏ e=(u,v)∈E ϕe(σu, σv) ϕ ϕv e u v G(V,E) • Ising/Potts model: ϕe(σu, σv) = { βe ∈ [0,1] if σu = σv 1 otherwise ϕe(σu, σv) = { 1 if σu = σv βe ∈ [0,1] otherwise ϕv is a distribution over [q] (ferromagnetic) (anti-ferromagnetic) or { (arbitrary local fields)