Normalizing Flow Regression

This repository provides the implementation and code used in the AABI 2025 (proceedings track) article Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations (Li et al., 2025).

• See the paper web page for more information.
• The full paper is available on arXiv and as Markdown files.

Overview

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.

Set up

conda env create -f environment.yml
conda activate nfr
# install kernel for jupyter notebook
python -m ipykernel install --user --name nfr

See demo.ipynb for an example of using NFR.

Citation

To appear in 7th Symposium on Advances in Approximate Bayesian Inference (AABI 2025, proceedings track).

Li, C., Huggins, B., Mikkola, P., & Acerbi, L. (2025). Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations. In 7th Symposium on Advances in Approximate Bayesian Inference.

BibTeX

@inproceedings{liNormalizingFlowRegression2025,
  title = {Normalizing Flow Regression for {B}ayesian Inference with Offline Likelihood Evaluations},
  booktitle = {7th Symposium on Advances in Approximate Bayesian Inference},
  author = {Li, Chengkun and Huggins, Bobby and Mikkola, Petrus and Acerbi, Luigi},
  year = {2025},
  note = {To appear},
  url = {https://approximateinference.org/2025/},
}

Acknowledgements

This repository includes code adapted from the nflows library: https://github.com/bayesiains/nflows, originally developed by Conor Durkan, Artur Bekasov, Iain Murray, and George Papamakarios.

We have modified nflows/transforms/autoregressive.py such that:

• When neural network parameters are zeros, the flow becomes the identity transform.
• The scale and shift transformation is constrained to a specified range.