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Sparse or $\ell_0$ adversarial attacks arbitrarily perturb an unknown subsetof the features. $\ell_0$ robustness analysis is particularly well-suited forheterogeneous (tabular) data where features have different types or scales.State-of-the-art $\ell_0$ certified defenses are based on randomized smoothingand apply to evasion attacks only. This paper proposes feature partitionaggregation (FPA) -- a certified defense against the union of $\ell_0$ evasion,backdoor, and poisoning attacks. FPA generates its stronger robustnessguarantees via an ensemble whose submodels are trained on disjoint featuresets. Compared to state-of-the-art $\ell_0$ defenses, FPA is up to3,000${\times}$ faster and provides larger median robustness guarantees (e.g.,median certificates of 13 pixels over 10 for CIFAR10, 12 pixels over 10 forMNIST, 4 features over 1 for Weather, and 3 features over 1 for Ames), meaningFPA provides the additional dimensions of robustness essentially for free.

Feature Partition Aggregation: A Fast Certified Defense Against a Union of $\ell_0$ Attacks