The Broader Landscape of Robustness in Algorithmic Statistics

Mean estimation is one of the most fundamental statistical tasks: given samples from a probability distribution, output an estimate of that distribution's mean. It is the prototypical question in statistical inference, and an important primitive that underlies a variety of more complex procedures (e.g., gradient descent, linear regression, etc.). In other words, understanding mean estimation is a prerequisite for understanding essentially any other inference task. As we will see, even in this basic setting, introducing new constraints or desiderata significantly affects the algorithmic ideas needed to solve the problem, particularly with a focus on computational efficiency. More precisely, mean estimation refers to the following statistical problem.