Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations

Chengkun Li, Bobby Huggins, Petrus Mikkola, Luigi Acerbi
Proceedings of the 7th Symposium on Advances in Approximate Bayesian Inference, PMLR 289:91-130, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v289-li25a, title = {Normalizing Flow Regression for {B}ayesian Inference with Offline Likelihood Evaluations}, author = {Li, Chengkun and Huggins, Bobby and Mikkola, Petrus and Acerbi, Luigi}, booktitle = {Proceedings of the 7th Symposium on Advances in Approximate Bayesian Inference}, pages = {91--130}, year = {2025}, editor = {Allingham, James Urquhart and Swaroop, Siddharth}, volume = {289}, series = {Proceedings of Machine Learning Research}, month = {29 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v289/main/assets/li25a/li25a.pdf}, url = {https://proceedings.mlr.press/v289/li25a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations %A Chengkun Li %A Bobby Huggins %A Petrus Mikkola %A Luigi Acerbi %B Proceedings of the 7th Symposium on Advances in Approximate Bayesian Inference %C Proceedings of Machine Learning Research %D 2025 %E James Urquhart Allingham %E Siddharth Swaroop %F pmlr-v289-li25a %I PMLR %P 91--130 %U https://proceedings.mlr.press/v289/li25a.html %V 289 %X 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.
APA
Li, C., Huggins, B., Mikkola, P. & Acerbi, L.. (2025). Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations. Proceedings of the 7th Symposium on Advances in Approximate Bayesian Inference, in Proceedings of Machine Learning Research 289:91-130 Available from https://proceedings.mlr.press/v289/li25a.html.

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