Varun Jog

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  A medley of geometry, optimal transport, and machine learning
  Varun Jog
  Modern machine learning algorithms are surprisingly fragile to adversarial perturbations of data. In this talk, we present some theoretical contributions towards understanding fundamental bounds on the performance of machine learning algorithms in the presence of adversaries. We shall discuss how optimal transport emerges as a natural mathematical tool to characterize "robust risk", which is a notion of risk in the adversarial machine learning literature that is analogous to Bayes risk in hypothesis testing. We shall also show how, in addition to tools from optimal transport, we may use reverse-isoperimetric inequalities from geometry to provide theoretical bounds on the sample size of estimating robust risk.