  We develop methods for efficient amortized approximate Bayesian inference
over posterior distributions of probabilistic clustering models, such as
Dirichlet process mixture models. The approach is based on mapping distributed,
symmetry-invariant representations of cluster arrangements into conditional
probabilities. The method parallelizes easily, yields iid samples from the
approximate posterior of cluster assignments with the same computational cost
of a single Gibbs sampler sweep, and can easily be applied to both conjugate
and non-conjugate models, as training only requires samples from the generative
model.
