Adaptive Robust Confidence Sets in High Dimensions
We study adaptive confidence sets for mean vectors of multivariate Gaussians with identity covariance under Huber contamination when the contamination proportion is unknown. We show that an information-theoretically optimal adaptive confidence set can be constructed by simultaneously quantifying uncertainty across all one-dimensional projections. The resulting confidence set achieves the optimal diameter and reveals a substantial adaptation cost compared with the minimax estimation error. Although statistically optimal, this construction is computationally infeasible. We establish a Statistical Query (SQ) lower bound showing that achieving diameter $O(m^{-1/2})$ requires either exponentia...
| Authors | Ilias Diakonikolas, Chao Gao, Daniel M. Kane et al. |
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| Primary category | math.ST |
| Published | 11 October 2026 |
| Last updated at source | 11 October 2026 |
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