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Resampling Base Distributions of Normalizing Flows

Overview

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions with a complex topological structure, such as Boltzmann distributions. Several procedures have been proposed to solve this problem but many of them sacrifice invertibility and, thereby, tractability of the log-likelihood as well as other desirable properties. To address these limitations, we introduce a base distribution for normalizing flows based on learned rejection sampling in our article Resampling Base Distributions of Normalizing Flows, allowing the resulting normalizing flow to model complex topologies without giving up bijectivity. In this repository, we implemented this class of base distributions and provide the script for various experiments comparing them to other commonly used base distributions. Some results of applying our method to 2D distributions are shown below.

This packages builds upon the normalizing flow library normflows. The Boltzmann generator experiments are realized via the boltzgen library.

Methods of Installation

The latest version of the package can be installed via pip

pip install --upgrade git+https://github.com/VincentStimper/resampled-base-flows.git

If you want to use a GPU, make sure that PyTorch is set up correctly by by following the instructions at the PyTorch website.

To run the Boltzmann generator experiments it is necessary to install OpenMM. Instructions on how to do this can be found here.

Citation

If you use our code in your own research, please cite our paper:

Vincent Stimper, Bernhard Schölkopf, José Miguel Hernández-Lobato. Resampling Base Distributions of Normalizing Flows. In Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, volume 151, pp. 4915–4936, 2022.

Bibtex

@inproceedings{Stimper2022,
  title = 	 {Resampling {B}ase {D}istributions of {N}ormalizing {F}lows},
  author =       {Vincent Stimper and Bernhard Sch{\"o}lkopf and Jos{\'e} Miguel Hern{\'a}ndez-Lobato},
  booktitle = 	 {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {4915--4936},
  year = 	 {2022},
  volume = 	 {151}
}