Being Robust (in High Dimensions) Can Be Practical
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:9991008, 2017.
Abstract
Robust estimation is much more challenging in highdimensions than it is in onedimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer science has shown that, in appropriate distributional models, it is possible to robustly estimate the mean and covariance with polynomial time algorithms that can tolerate a constant fraction of corruptions, independent of the dimension. However, the sample and time complexity of these algorithms is prohibitively large for highdimensional applications. In this work, we address both of these issues by establishing sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions. Finally, we show on both synthetic and real data that our algorithms have stateoftheart performance and suddenly make highdimensional robust estimation a realistic possibility.
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