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About this paper
Antonin Schrab, Ilmun Kim
The paper introduces corruption-aware permutation tests that tolerate a user-specified number of arbitrarily replaced observations without identifying them. They raise the rejection threshold by a sensitivity-based buffer, providing finite-sample type-I control. In a synthetic example, dcMMD detects differences with 2,000 samples while allowing 800 corruptions; its separation rate matches the uncorrupted rate only at low corruption and is minimax-optimal under stated assumptions.
Key insights
- The DC procedure provides non-asymptotic Type I error control for any test statistic with finite global sensitivity, ensuring statistical validity even with arbitrary corruption of up to 'r' data points.
- The developed dcMMD and dcHSIC tests achieve minimax optimal uniform separation rates, quantifying the minimum detectable difference between distributions across various corruption levels (low, high, and total corruption regimes).
- Empirical comparisons demonstrate that DC tests maintain robust error control and exhibit significantly higher power in detecting alternatives compared to robust tests based on differentially private procedures.
Summary by alphaXiv.
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