Understanding and Accelerating Particle-Based Variational Inference
This work addresses the challenge of making Bayesian inference more efficient and accurate for researchers and practitioners in machine learning, though it is incremental in building on existing particle-based methods.
The paper tackled the problem of improving particle-based variational inference methods by analyzing them through Wasserstein gradient flows, leading to a unified theoretical understanding and new practical methods. The results showed improved convergence and enhanced sample accuracy in experiments.
Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify various finite-particle approximations that existing ParVIs use, and recognize that the approximation is essentially a compulsory smoothing treatment, in either of two equivalent forms. This novel understanding reveals the assumptions and relations of existing ParVIs, and also inspires new ParVIs. We propose an acceleration framework and a principled bandwidth-selection method for general ParVIs; these are based on the developed theory and leverage the geometry of the Wasserstein space. Experimental results show the improved convergence by the acceleration framework and enhanced sample accuracy by the bandwidth-selection method.