NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
This addresses a bottleneck in Bayesian inference for practitioners dealing with complex posterior distributions, though it is an incremental improvement combining existing techniques.
The paper tackles the problem of slow convergence and mixing in Hamiltonian Monte Carlo (HMC) due to unfavorable posterior geometry by proposing NeuTra HMC, which uses neural transport with inverse autoregressive flows to warp the space, resulting in significant improvements in time to stationarity and effective-sample-size rates.
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.