  Recently, particle-based variational inference (ParVI) methods have gained
interest because they directly minimize the Kullback-Leibler divergence and do
not suffer from approximation errors from the evidence-based lower bound.
However, many ParVI approaches do not allow arbitrary sampling from the
posterior, and the few that do allow such sampling suffer from suboptimality.
This work proposes a new method for learning to approximately sample from the
posterior distribution. We construct a neural sampler that is trained with the
functional gradient of the KL-divergence between the empirical sampling
distribution and the target distribution, assuming the gradient resides within
a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach
maintains the asymptotic performance of ParVI methods while offering the
flexibility of a generative sampler. Through carefully constructed experiments,
we show that GPVI outperforms previous generative ParVI methods such as
amortized SVGD, and is competitive with ParVI as well as gold-standard
approaches like Hamiltonian Monte Carlo for fitting both exactly known and
intractable target distributions.
