Over the last few years, there has been significant theoretical work in robust high-dimensional statistical estimation. These results seem aligned with modern goals in practical machine learning, where high-dimensional data is ubiquitous, and robustness and security are paramount. This raises the question: are these advances purely theoretical, or can we reap their benefits in the real world? In this talk, I will describe some first steps towards answering this question positively, including evidence that these theoretical advances may be realizable. I will discuss applications to exploratory data analysis and robust stochastic optimization on synthetic and real-world datasets.

Based on joint works with Ilias Diakonikolas, Daniel Kane, Jerry Li, Ankur Moitra, Jacob Steinhardt, and Alistair Stewart. Papers available at https://arxiv.org/abs/1703.00893 and https://arxiv.org/abs/1803.02815.