Robust Mean Estimation within the Domain of Computational Tractability

The estimation of the mean vector is fundamental statistical problem, which has been studied carefully in the literature. The question becomes more interesting when it is known that some small portion of observations are corrupted by the nature, i.e. there are outliers in the dataset. This is a very interesting and hard question, since in the modern era where more and more datasets are becoming available the outliers are inevitable. The simple folklore estimators sample mean and sample median perform poorly for large outliers and scale poorly with the growth of dimension, respectively. However, they are easy-to-compute which is essential in machine learning applications. So to sum up, the goal of this project is to make progress in the field of robust mean estimation within the domain of computational tractability based on the research that have been conducted by authors in the past 2 years. The field of robust statistics is very promising and not limited by robust mean estimation. This field is fairly popular with many interesting open problems.