Speaker
Description
Recent work in machine learning has recognized that many standard algorithms for classification are strongly affected by adversarial attacks. Accordingly, a growing body of research has tried to identify ways to mitigate this issue. This talk will discuss a natural non-parametric formulation of this objective, which can be transformed into a standard classification problem that utilizes a non-local perimeter as a regularizer. I'll discuss recent work which i) establishes smoothness of classification boundaries under mild assumptions and ii) quantifies the degree to which adversarial attacks will modify the Bayes classifier. Connections with optimal transportation, mean curvature flow, and minimal surfaces, and related open problems will also be discussed.