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Collective Robustness Certificates

Reference implementation of the certificate proposed in

"Collective Robustness Certificates: Exploiting Interdependence in Graph Neural Networks"
Jan Schuchardt, Aleksandar Bojchevski, Johannes Klicpera, and Stephan Günnemann, ICLR 2021.

Usage

To use the certificate you need to provide the following data:

• A binary attributed graph consisting of an attribute and an adjacency matrix.
• A boolean array corresponding to prediction-wise base certificates where
  • Each element of the first dimension corresponds to a different prediction / node,
  • The d trailing dimensions correspond to different perturbation types.
• A list of d strings from {adj_del, attr_add, attr_del}, indicating which of the trailing dimensions corresponds to which perturbation type .
• A list of d binary sparse matrices characterizing each prediction's receptive field.
  • Shape (n, n) for attribute perturbations.
  • Shape (n, |E|) for edge deletions, where |E| is number of existing edges.

The notebook demo.ipynb provides an usage example with pre-calculated base certificates based on randomized smoothing.
Our method works with any cvxpy-compatible optimizer, but we recommend using a commercial solver (e.g. MOSEK or GUROBI) for improved efficiency.

Cite

Please cite our paper if you use this code in your own work:

@InProceedings{Schuchardt2021_Collective,
  author = {Schuchardt, Jan and Klicpera, Johannes and Bojchevski, Aleksandar and G{\"u}nnemann, Stephan},
  title     = {Collective Robustness Certificates: Exploiting Interdependence in Graph Neural Networks},
  booktitle = {International Conference on Learning Representations},
  year      = {2021},
}