Variational Particle Approximations

Monte Carlo methods provide a powerful framework for approximating probability distributions with a set of stochastically sampled particles. In this paper, we rethink particle approximations from the perspective of variational inference, where the particles play the role of variational parameters. This leads to a deterministic version of Monte Carlo in which the particles are selected to optimize the Kullback-Leibler divergence between the approximation and the target distribution. Variational particle approximations overcome some of the weaknesses of Monte Carlo methods like particle filtering, leading to substantially improved performance on several synthetic and real-world datasets.