Evolving-Graph Gaussian Processes

Evolving-Graph Gaussian Processes (e-GGPs) model the evolution of graph nodes via a GP. The method uses a kernel that considers the neighbourhood and node attributes of the graph. The e-GGP code provided here can be used for regression tasks on dynamic graphs.

If you find this code useful, please consider citing:

@article{blancomulero2021evolvinggraph,
      title={Evolving-Graph Gaussian Processes}, 
      author={David Blanco-Mulero and Markus Heinonen and Ville Kyrki},
      year={2021},
      journal={arXiv preprint arXiv:2106.15127},
      eprint={2106.15127},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

Model structure

The repository contains the following:

• e_ggp/evolving_gp.py - e-GGP model.
• e_ggp/kernels.py - attributed sub-tree kernel used in e-GGP .
• train_eggp.py - script for training e-GGP using one of the given datasets.

The e_ggp/kernels.py file contains an implementation of the kernel used in the paper:

$$k_{nn}(\mathbf{v}_i, \mathbf{v}_j) = \dfrac{1}{L} \sum\limits_{\mathbf{x}_i \in N_i^1} \sum\limits_{\mathbf{x}_j \in N^1_j} k_l(\varphi_\mathbf{v}(\mathbf{x}_{i}), \varphi_\mathbf{v}(\mathbf{x}_{j})).$$ $$K(\mathbf{v}_i,\mathbf{v}_j) = k_r(\varphi_\mathbf{v}(\mathbf{v}_{i}), \varphi_\mathbf{v}(\mathbf{v}_{j})) + k_{nn}(\mathbf{v}_i, \mathbf{v}_j).$$

We also provide utils that are used for selecting the training points, creating the datasets as well as plot utils in the folder e_ggp/utils.

Requirements

The code is mainly based on GPyTorch and uses Python-igraph for defining the graphs.

To install the requirements you can run

pip install --user -r requirements.txt

Usage

You can run the training for the graph interaction dataset with:

python3 train_eggp.py  -df datasets/graph_interaction_origin.npy
-dt datasets/graph_interaction_test/ --new_dataset

For an estimation of the training time we encourage you to have a look at the paper Supplementary material section.

We provide a Jupyter Notebook as well as more detailed instructions on how to train the given datasets using our model.

If you want to use your own dataset take a look at the GraphInteraction and IsolatedSubgraphs classes which inherit from GraphDataset in datasets.py.

Environments

We provide the datasets of the two environments used in the paper in datasets/.

Graph-Interaction environment	Isolated evolving sub-graphs environment

The Graph-Interaction environment is based on MuJoCo-Py.

The code for the isolated evolving sub-graphs environment can be found in environments/water_2d.py.

The environment is based on Taichi-MPM and Taichi-elements