Hamiltonian ABC

Approximate Bayesian computation (ABC) is a
powerful and elegant framework for performing
inference in simulation-based models. However,
due to the difficulty in scaling likelihood estimates,
ABC remains useful for relatively lowdimensional
problems. We introduce Hamiltonian
ABC (HABC), a set of likelihood-free
algorithms that apply recent advances in scaling
Bayesian learning using Hamiltonian Monte
Carlo (HMC) and stochastic gradients. We find
that a small number forward simulations can effectively
approximate the ABC gradient, allowing
Hamiltonian dynamics to efficiently traverse
parameter spaces. We also describe a new simple
yet general approach of incorporating random
seeds into the state of the Markov chain, further
reducing the random walk behavior of HABC.
We demonstrate HABC on several typical ABC
problems, and show that HABC samples comparably
to regular Bayesian inference using true
gradients on a high-dimensional problem from
machine learning.