  Hamiltonian Monte Carlo is a powerful algorithm for sampling from
difficult-to-normalize posterior distributions. However, when the geometry of
the posterior is unfavorable, it may take many expensive evaluations of the
target distribution and its gradient to converge and mix. We propose neural
transport (NeuTra) HMC, a technique for learning to correct this sort of
unfavorable geometry using inverse autoregressive flows (IAF), a powerful
neural variational inference technique. The IAF is trained to minimize the KL
divergence from an isotropic Gaussian to the warped posterior, and then HMC
sampling is performed in the warped space. We evaluate NeuTra HMC on a variety
of synthetic and real problems, and find that it significantly outperforms
vanilla HMC both in time to reach the stationary distribution and asymptotic
effective-sample-size rates.
