Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations
This addresses the problem of computationally prohibitive Bayesian inference for researchers in scientific domains like neuroscience and biology, offering an incremental improvement by leveraging existing evaluations.
The paper tackles the challenge of Bayesian inference with computationally expensive likelihood evaluations by proposing normalizing flow regression (NFR), a novel offline method that directly approximates posterior distributions from existing log-density evaluations, demonstrating superior or comparable performance on synthetic benchmarks and real-world applications in neuroscience and biology.
Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior distributions. Unlike traditional surrogate approaches that require additional sampling or inference steps, NFR directly yields a tractable posterior approximation through regression on existing log-density evaluations. We introduce training techniques specifically for flow regression, such as tailored priors and likelihood functions, to achieve robust posterior and model evidence estimation. We demonstrate NFR's effectiveness on synthetic benchmarks and real-world applications from neuroscience and biology, showing superior or comparable performance to existing methods. NFR represents a promising approach for Bayesian inference when standard methods are computationally prohibitive or existing model evaluations can be recycled.