  We consider the problem of inference in a causal generative model where the
set of available observations differs between data instances. We show how
combining samples drawn from the graphical model with an appropriate masking
function makes it possible to train a single neural network to approximate all
the corresponding conditional marginal distributions and thus amortize the cost
of inference. We further demonstrate that the efficiency of importance sampling
may be improved by basing proposals on the output of the neural network. We
also outline how the same network can be used to generate samples from an
approximate joint posterior via a chain decomposition of the graph.
