Likelihood-free MCMC with Amortized Approximate Ratio Estimators

2019/03/10 by Joeri Hermans, Hermans, Joeri, Volodimir Begy +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Model Reduction and Neural Networks #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1903.04057

v5: Camera-ready version presented at ICML 2020

openalex publication_date 2019/03/10 · arxiv created 2020/06/26 · arxiv updated 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Approximating Likelihood Ratios with Calibrated Discriminative Classifiers
• Very Deep Convolutional Networks for Large-Scale Image Recognition
• Gradient-based learning applied to document recognition
• Monte Carlo sampling methods using Markov chains and their applications
• Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)
• A Conceptual Introduction to Hamiltonian Monte Carlo
• Validating Bayesian Inference Algorithms with Simulation-Based Calibration
• Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation

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