A heat-bath based algorithm [Feng,Guo,Y.'19] ibbs distribution:u(o)cΠAe(o,a,)Πb,(a,) e={u,v}∈E v∈V current sample:u RvVv is updated or incident to updated e); while R≠☑do pick a random u∈R; constant factor depends only on with probability do ur(XuI XN) XRONG) resampleIXND): heat-bath delete u from R; a.k.a.Glauber dynamics Gibbs sampling else add all neighbors of u to R; N(w≌neighborhood of uA heat-bath based algorithm ; while do pick a random ; with probability do resample ; delete from ; else add all neighbors of to ; R ← {v ∈ V ∣ v is updated or incident to updated e} R ≠ ∅ u ∈ R ∝ 1 μu(Xu ∣ XN(u)) Xu ∼ μu( ⋅ ∣ XN(u) ) u R u R heat-bath a.k.a. Glauber dynamics Gibbs sampling constant factor depends only on XR∩N(u) [Feng, Guo, Y. ’19] Gibbs distribution: μ(σ) ∝ ∏ e={u,v}∈E Ae (σu, σv)∏ v∈V bv (σv) current sample: X ∼ μ N(u) ≜ neighborhood of u