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Existing techniques for certifying the robustness of models for discrete dataeither work only for a small class of models or are general at the expense ofefficiency or tightness. Moreover, they do not account for sparsity in theinput which, as our findings show, is often essential for obtaining non-trivialguarantees. We propose a model-agnostic certificate based on the randomizedsmoothing framework which subsumes earlier work and is tight, efficient, andsparsity-aware. Its computational complexity does not depend on the number ofdiscrete categories or the dimension of the input (e.g. the graph size), makingit highly scalable. We show the effectiveness of our approach on a wide varietyof models, datasets, and tasks -- specifically highlighting its use for GraphNeural Networks. So far, obtaining provable guarantees for GNNs has beendifficult due to the discrete and non-i.i.d. nature of graph data. Our methodcan certify any GNN and handles perturbations to both the graph structure andthe node attributes.

Efficient Robustness Certificates for Discrete Data: Sparsity-Aware Randomized Smoothing for Graphs, Images and More