Reparameterized Variational Rejection Sampling
Martin Jankowiak Du Phan
Traditional approaches to variational inference rely on parametric families
of variational distributions, with the choice of family playing a critical role
in determining the accuracy of the resulting posterior approximation. Simple
mean-field families often lead to poor approximations, while rich families of
distributions like normalizing flows can be difficult to optimize and usually
do not incorporate the known structure of the target distribution due to their
black-box nature. To expand the space of flexible variational families, we
revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which
combines a parametric proposal distribution with rejection sampling to define a
rich non-parametric family of distributions that explicitly utilizes the known
target distribution. By introducing a low-variance reparameterized gradient
estimator for the parameters of the proposal distribution, we make VRS an
attractive inference strategy for models with continuous latent variables. We
argue theoretically and demonstrate empirically that the resulting
method--Reparameterized Variational Rejection Sampling (RVRS)--offers an
attractive trade-off between computational cost and inference fidelity. In
experiments we show that our method performs well in practice and that it is
well-suited for black-box inference, especially for models with local latent
variables.