  We present a variational inference (VI) framework that unifies and leverages
sequential Monte-Carlo (particle filtering) with \emph{approximate} rejection
sampling to construct a flexible family of variational distributions.
Furthermore, we augment this approach with a resampling step via Bernoulli
race, a generalization of a Bernoulli factory, to obtain a low-variance
estimator of the marginal likelihood. Our framework, Variational Rejection
Particle Filtering (VRPF), leads to novel variational bounds on the marginal
likelihood, which can be optimized efficiently with respect to the variational
parameters and generalizes several existing approaches in the VI literature. We
also present theoretical properties of the variational bound and demonstrate
experiments on various models of sequential data, such as the Gaussian
state-space model and variational recurrent neural net (VRNN), on which VRPF
outperforms various existing state-of-the-art VI methods.
