Robust Mean Estimation in High Dimensions: An Outlier-Fraction Agnostic and Efficient Algorithm

The problem of robust mean estimation in high dimensions is studied, which a certain fraction (less than half) the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, formulated as minimization ℓ 0 -‘norm’ an outlier indicator vector , under second moment constraint on datapoints. then relaxed to xmlns:xlink="http://www.w3.org/1999/xlink">p -norm (0 < xmlns:xlink="http://www.w3.org/1999/xlink">p ≤ 1) objective, and it shown that global minima for each these objectives are order-optimal have optimal breakdown point problem. Furthermore, computationally tractable iterative -minimization hard thresholding algorithm proposed outputs estimate population mean. (with ≈ 0.3) does not require prior knowledge outliers, contrast with most existing algorithms, = 1 has near-linear time complexity. Both synthetic real data experiments demonstrate outperforms state-of-the-art methods.