In every corner of machine learning and statistics, there is a need for estimators that work not just in an idealized model but even when their assumptions are violated. It turns out that being provably robust and being efficiently computable are often at odds with each other. In even the most basic settings such as robustly computing the mean and covariance, until recently the only known estimators were either hard to compute or could only tolerate a negligible fraction of errors in high-dimensional applications.

In this tutorial, we will survey the exciting recent progress in algorithmic robust statistics. We will give the first provably robust and efficiently computable estimators for several fundamental questions that were thought to be hard, and explain the main insights behind them. We will give practical applications to exploratory data analysis. Finally, we raise some philosophical questions about robustness. It is standard to compare algorithms (especially those with provable guarantees) in terms of their running time and sample complexity. But what frameworks can be used to explore their robustness?