Adversarial Classification: Necessary conditions and geometric flows
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We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance ε, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as ε varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension we rigorously prove that one can use the initial value problem starting from ε=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem. Numerical examples illustrating these ideas are also presented.
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