Abstract:
Motivated by data perturbation, adversarial training has recently been proposed as a new way of parameter estimation in supervised learning. This talk will discuss the statistical properties of the adversarial training estimator from both asymptotic and non- asymptotic perspectives. Firstly, the asymptotic distribution of the adversarial training estimator will be introduced, based on which a new technique has been proposed to improve the performance of existing adversarial training. Secondly, the non-asymptotic convergence rate of the adversarial training estimator will be discussed. The results show that the adversarial training estimator is minimax optimal under $\ell_\infty$- perturbations in high dimensional linear regression. My research aims to provide an understanding of emerging methods in machine learning and artificial intelligence, particularly from their statistical performance perspective. I will discuss some potential future topics.

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