Code for "Fast post-process Bayesian inference with Variational Sparse Bayesian Quadrature"

Variational Sparse Bayesian Quadrature (VSBQ) is a fast post-process Bayesian inference method for (potentially expensive) Bayesian models. It operates by recycling existing likelihood/density evaluations (e.g., from maximum-a-posteriori (MAP) optimization runs), fitting a regression surrogate (a sparse Gaussian process), and conducting variational inference to get a posterior approximation. Our current implementation is based on PyVBMC. benchflow is a toolkit for running the benchmark experiments in the paper.

Installation

conda create -n vsbq python=3.9
conda activate vsbq
pip install -e ./benchflow
pip install -e ./pyvbmc
# Install the kernel for Jupyter
python -m ipykernel install --user --name vsbq 

Example

See the example notebook for a simple example of using VSBQ.

Citation

Please cite our paper if you find this work useful:

@article{liFastPostprocessBayesian2025,
  title = {Fast Post-Process {{Bayesian}} Inference with Variational Sparse {{Bayesian}} Quadrature},
  author = {Li, Chengkun and Clart{\'e}, Gr{\'e}goire and J{\o}rgensen, Martin and Acerbi, Luigi},
  year = 2025,
  month = aug,
  journal = {Statistics and Computing},
  volume = {35},
  number = {6},
  pages = {167},
  issn = {1573-1375},
  doi = {10.1007/s11222-025-10695-7},
  langid = {english}
}