dgpsi

A Python package for deep and linked Gaussian process emulations

dgpsi currently implements:

• Deep Gaussian process emulation with flexible architecture construction:
  • multiple layers;
  • multiple GP nodes;
  • separable or non-separable squared exponential and Matérn2.5 kernels;
  • global input connections;
  • non-Gaussian likelihoods (Poisson, Negative-Binomial, heteroskedastic Gaussian, and more to come);
• Linked emulation of feed-forward systems of computer models:
  • linking GP emulators of deterministic individual computer models;
  • linking GP and DGP emulators of deterministic individual computer models;
• Multi-core predictions from GP, DGP, and Linked (D)GP emulators;
• Fast Leave-One-Out (LOO) cross validations for GP and DGP emulators.

For R users

The R interface to the package is available at dgpsi-R.

Installation

dgpsi currently requires Python version 3.7, 3.8, or 3.9. The package can be installed via pip:

pip install dgpsi

or conda:

conda install -c conda-forge dgpsi

However, to gain the best performance of the package or you are using an Apple Silicon computer, we recommend the following steps for the installation:

• Download and install Miniforge3 that is compatible to your system from here.
• Run the following command in your terminal app to create a virtual environment called dgp_si:

conda create -n dgp_si python=3.9.13 

• Activate and enter the virtual environment:

conda activate dgp_si

• Install dgpsi:

  • for Apple Silicon users, you could gain speed-up by switching to Apple's Accelerate framework:

  conda install dgpsi "libblas=*=*accelerate"
  

  • for Intel users, you could gain speed-up by switching to MKL:

  conda install dgpsi "libblas=*=*mkl"
  

  • otherwise, simply run:

  conda install dgpsi
  

Demo and documentation

Please see demo for some illustrative examples of the method. The API reference of the package can be accessed from https://dgpsi.readthedocs.io, and some tutorials will be soon added there.

Tips

• Since SI is a stochastic inference, in case of unsatisfactory results, you may want to try to restart the training multiple times even with initial values of hyperparameters unchanged;
• The recommended DGP structure is a two-layered one with the number of GP nodes in the first layer equal to the number of input dimensions (i.e., number of input columns) and the number of GP nodes in the second layer equal to the number of output dimensions (i.e., number of output columns) or the number of parameters in the specified likelihood. The dgp class in the package is default to this structure.

Contact

Please feel free to email me with any questions and feedbacks:

Deyu Ming <deyu.ming.16@ucl.ac.uk>.

References

Ming, D., Williamson, D., and Guillas, S. (2022) Deep Gaussian process emulation using stochastic imputation. Technometrics (to appear).

Ming, D. and Guillas, S. (2021) Linked Gaussian process emulation for systems of computer models using Matérn kernels and adaptive design, SIAM/ASA Journal on Uncertainty Quantification. 9(4), 1615-1642.