  Learning in the presence of outliers is a fundamental problem in statistics.
Until recently, all known efficient unsupervised learning algorithms were very
sensitive to outliers in high dimensions. In particular, even for the task of
robust mean estimation under natural distributional assumptions, no efficient
algorithm was known. Recent work in theoretical computer science gave the first
efficient robust estimators for a number of fundamental statistical tasks,
including mean and covariance estimation. Since then, there has been a flurry
of research activity on algorithmic high-dimensional robust estimation in a
range of settings. In this survey article, we introduce the core ideas and
algorithmic techniques in the emerging area of algorithmic high-dimensional
robust statistics with a focus on robust mean estimation. We also provide an
overview of the approaches that have led to computationally efficient robust
estimators for a range of broader statistical tasks and discuss new directions
and opportunities for future work.
