This repository contains the python code that was presented for the following paper.

[1] Adachi, M., Hayakawa, S., Jørgensen, M., Oberhauser, H., and Osborne, M. A. Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination. Advances in Neural Information Processing Systems 35 (NeurIPS 2022), 2022

• fast batch Bayesian quadrature
• GPU acceleration
• Arbitrary kernel for Bayesian quadrature modelling
• Arbitrary prior distribution for Bayesian inference

BASQ can sample more diversely and quickly than the existing batch Bayesian Quadrature method (batch WSABI). The data presented in the paper was coded with GPy, which is based on batch WSABI code for comparison. The GPy one is not fast as we won't open but I can share if necessary. Batch WSABI code is here: link

• PyTorch
• GPyTorch
• BoTorch

python3 main.py

The example with Gaussian Mixture Likelihood (dim=10) will run.

You can select arbitrary kernels/priors/parameters on ./BASQ/_parametetrs.py

• To change kernel: change "kernel_type", such as Matern52.
• To change prior: change the prior distribution directly as input to the BASQ. The prior must be defined by torch.distributions (see main.py)
• As WSABI and uncertainty sampling is defined only for RBF kernel and normal prior, non-Gaussian kernel or prior will raise errors.

Please cite this work as

@article{adachi2022fast,
  title={Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination},
  author={Adachi, Masaki and Hayakawa, Satoshi and Jørgensen, Martin and Oberhauser, Harald and Osborne, Michael A.},
  journal={Advances in Neural Information Processing Systems 35 (NeurIPS 2022)},
  year={2022}
}