Accelerated First-order Methods on the Wasserstein Space for Bayesian Inference
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We consider doing Bayesian inference by minimizing the KL divergence on the 2-Wasserstein space P_2. By exploring the Riemannian structure of P_2, we develop two inference methods by simulating the gradient flow on P_2 via updating particles, and an acceleration method that speeds up all such particle-simulation-based inference methods. Moreover we analyze the approximation flexibility of such methods, and conceive a novel bandwidth selection method for the kernel that they use. We note that P_2 is quite abstract and general so that our methods can make closer approximation, while it still has a rich structure that enables practical implementation. Experiments show the effectiveness of the two proposed methods and the improvement of convergence by the acceleration method.
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