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• W3109042425 abstract "We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance $varepsilon$, 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 $varepsilon$ 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 $varepsilon=0$, 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." @default.
• W3109042425 created "2020-12-07" @default.
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• W3109042425 creator A5073143742 @default.
• W3109042425 date "2020-11-21" @default.
• W3109042425 modified "2023-09-27" @default.
• W3109042425 title "Adversarial Classification: Necessary conditions and geometric flows." @default.
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• W3109042425 hasPublicationYear "2020" @default.
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