  Neural network classifiers are vulnerable to data poisoning attacks, as
attackers can degrade or even manipulate their predictions thorough poisoning
only a few training samples. However, the robustness of heuristic defenses is
hard to measure. Random selection based defenses can achieve certified
robustness by averaging the classifiers' predictions on the sub-datasets
sampled from the training set. This paper proposes a framework of random
selection based certified defenses against data poisoning attacks.
Specifically, we prove that the random selection schemes that satisfy certain
conditions are robust against data poisoning attacks. We also derive the
analytical form of the certified radius for the qualified random selection
schemes. The certified radius of bagging derived by our framework is tighter
than the previous work. Our framework allows users to improve robustness by
leveraging prior knowledge about the training set and the poisoning model.
Given higher level of prior knowledge, we can achieve higher certified accuracy
both theoretically and practically. According to the experiments on three
benchmark datasets: MNIST 1/7, MNIST, and CIFAR-10, our method outperforms the
state-of-the-art.
