Likelihood-free MCMC with Amortized Approximate Ratio Estimators

Abstract

Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing practitioners to make use of approximations. This work introduces a novel approach to address the intractability of the likelihood and the marginal model. We achieve this by learning a flexible amortized estimator which approximates the likelihood-to-evidence ratio. We demonstrate that the learned ratio estimator can be embedded in MCMC samplers to approximate likelihood-ratios between consecutive states in the Markov chain, allowing us to draw samples from the intractable posterior. Techniques are presented to improve the numerical stability and to measure the quality of an approximation. The accuracy of our approach is demonstrated on a variety of benchmarks against well-established techniques. Scientific applications in physics show its applicability.

arXiv commentv5: Camera-ready version presented at ICML 2020

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Cited by in corpus (9)

• Machine learning and the physical sciences
• The frontier of simulation-based inference
• Mining gold from implicit models to improve likelihood-free inference
• Mining for Dark Matter Substructure: Inferring subhalo population properties from strong lenses with machine learning
• Towards constraining warm dark matter with stellar streams through neural simulation-based inference
• Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy
• Targeted Likelihood-Free Inference of Dark Matter Substructure in Strongly-Lensed Galaxies
• Diagnosing model misspecification and performing generalized Bayes' updates via probabilistic classifiers
• Probabilistic elicitation of expert knowledge through assessment of computer simulations