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Parallelization Glauber dynamics: starting from an arbitrary Xo E [g] G(V,E): transition for XX+1: pick a uniform random vertex v; resample X(v)according to the marginal distribution induced by u at vertex v conditioning on Xi(N(v)); Parallelization: ● Chromatic scheduler [folklore][Gonzalez et al.,AISTAT'11]: Vertices in the same color class are updated in parallel. "Hogwild!"[Niu,Recht,Re,Wright,NIPS'11]De Sa,Olukotun,Re,ICML16]: All vertices are updated in parallel,ignoring concurrency issues.Parallelization G(V,E): v Glauber dynamics: Parallelization: • Chromatic scheduler [folklore] [Gonzalez et al., AISTAT’11]: Vertices in the same color class are updated in parallel. • “Hogwild!” [Niu, Recht, Ré, Wright, NIPS’11][De Sa, Olukotun, Ré, ICML’16]: All vertices are updated in parallel, ignoring concurrency issues. pick a uniform random vertex v; resample X(v) according to the marginal distribution induced by µ at vertex v conditioning on Xt(N(v)); starting from an arbitrary X0 ∈ [q]V transition for Xt → Xt+1 :
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