Likelihood-free MCMC with Amortized Approximate Likelihood Ratios
Year: 2019
Type: preprint
Abstract: Posterior inference with an intractable likelihood is becoming anincreasingly common task in scientific domains which rely on sophisticated
computer simulations. Typically, these mechanistic models do not admit
tractable densities forcing practitioners to rely on approximations during
inference. This work proposes a novel approach to address the intractability of
the likelihood and the marginal model. We achieve this by learning a flexible
estimator which approximates the likelihood-to-evidence ratio. The resulting
amortized ratio estimator is embedded in MCMC samplers such as
Metropolis-Hastings and Hamiltonian Monte Carlo to approximate the
likelihood-ratio between consecutive states in the Markov chain, allowing us to
draw samples from the intractable posterior. Techniques are presented to
improve the numerical stability. We demonstrate our approach on a variety of
benchmarks and compare against well-established approximate inference
techniques. Scientific applications in high energy and astrophysics with
high-dimensional observations show its applicability.
Source: arXiv (Cornell University)
Authors: Joeri Hermans, Volodimir Begy, Gilles Louppe
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3180716327