Sampling from high-dimensional distributions poses significant computational challenges. We introduce Subspace Langevin Monte Carlo (SLMC), a novel and efficient sampling method that generalizes coordinate and preconditioned Langevin Monte Carlo. At a higher level, our method can be viewed as a natural extension of subspace descent techniques from Euclidean space to Wasserstein space. If time permits, we will discuss subspace Wasserstein descent in other settings.
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