The following paper represents the beginning of a long and productive line of work on robust statistics in high dimensions. While robust statistics has long been studied, going back at least to Tukey,6 the recent revival centers on algorithmic questions that were largely unaddressed by the earlier statistical work.
Robust statistics centers on the question of how to extract information from data that may have been corrupted in some way. The most common form of robustness, also considered here, is robust to outliers: some fraction of the data has been removed and replaced with arbitrary, erroneous points. A familiar instance of robust statistics is using the median instead of the mean, since the median is less sensitive to extreme points, while in contrast a single overly large value could completely skew the mean.
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