Collective Certified Robustness against Graph Injection Attacks
Yuni Lai Bailin Pan Kaihuang Chen Yancheng Yuan Kai Zhou
We investigate certified robustness for GNNs under graph injection attacks.
Existing research only provides sample-wise certificates by verifying each node
independently, leading to very limited certifying performance. In this paper,
we present the first collective certificate, which certifies a set of target
nodes simultaneously. To achieve it, we formulate the problem as a binary
integer quadratic constrained linear programming (BQCLP). We further develop a
customized linearization technique that allows us to relax the BQCLP into
linear programming (LP) that can be efficiently solved. Through comprehensive
experiments, we demonstrate that our collective certification scheme
significantly improves certification performance with minimal computational
overhead. For instance, by solving the LP within 1 minute on the Citeseer
dataset, we achieve a significant increase in the certified ratio from 0.0% to
81.2% when the injected node number is 5% of the graph size. Our step marks a
crucial step towards making provable defense more practical.