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Bootstrap aggregating (bagging) is an effective ensemble protocol, which isbelieved can enhance robustness by its majority voting mechanism. Recent worksfurther prove the sample-wise robustness certificates for certain forms ofbagging (e.g. partition aggregation). Beyond these particular forms, in thispaper, \emph{we propose the first collective certification for general baggingto compute the tight robustness against the global poisoning attack}.Specifically, we compute the maximum number of simultaneously changedpredictions via solving a binary integer linear programming (BILP) problem.Then we analyze the robustness of vanilla bagging and give the upper bound ofthe tolerable poison budget. Based on this analysis, \emph{we propose hashbagging} to improve the robustness of vanilla bagging almost for free. This isachieved by modifying the random subsampling in vanilla bagging to a hash-baseddeterministic subsampling, as a way of controlling the influence scope for eachpoisoning sample universally. Our extensive experiments show the notableadvantage in terms of applicability and robustness.

On Collective Robustness of Bagging Against Data Poisoning