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I will talk about the algorithmic version of the phenomenon of measure concentration: in many high dimensional probability spaces, for subsets of the space of non-negligible mass, most of the points in the space are very close to at least one point in the subset. We will give an algorithm called MUCIO (MUltiplicative Conditional Influence Optimizer) that efficient-ly finds one such point with high probability. Then we discuss the implication of this algorithm for the security of machine learning: how it may help an adversary change the distribution of the training set so that a classifier makes an error. This is joint work with Mohammad Mahmoody and Saeed Mahloujifar, and appears in SODA 2020.

Researcher at Institute for Research in Fundamental Sciences (IPM) in Iran