Hamiltonian ABC
This work addresses a bottleneck in simulation-based inference for researchers in statistics and machine learning, offering a novel method that is incremental but improves scalability.
The paper tackles the challenge of scaling Approximate Bayesian Computation (ABC) to high-dimensional problems by introducing Hamiltonian ABC (HABC), which leverages Hamiltonian Monte Carlo and stochastic gradients to efficiently traverse parameter spaces with few simulations, achieving performance comparable to true gradient methods on a high-dimensional machine learning task.
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 low-dimensional 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.