Title: Forward Amortized Inference for Likelihood-Free Variational Marginalization,
Abstract: In this paper, we introduce a new form of amortized variational inference by
using the forward KL divergence in a joint-contrastive variational loss. The
resulting forward amortized variational inference is a likelihood-free method
as its gradient can be sampled without bias and without requiring any
evaluation of either the model joint distribution or its derivatives. We prove
that our new variational loss is optimized by the exact posterior marginals in
the fully factorized mean-field approximation, a property that is not shared
with the more conventional reverse KL inference. Furthermore, we show that
forward amortized inference can be easily marginalized over large families of
latent variables in order to obtain a marginalized variational posterior. We
consider two examples of variational marginalization. In our first example we
train a Bayesian forecaster for predicting a simplified chaotic model of
atmospheric convection. In the second example we train an amortized variational
approximation of a Bayesian optimal classifier by marginalizing over the model
space. The result is a powerful meta-classification network that can solve
arbitrary classification problems without further training.