New HOMER algorithm boosts AI robustness with Huber-of-Means

Heavy tails weaken high-confidence control for the empirical mean, and geometric median-of-means lacks a threshold that moves toward mean efficiency. To address this, Kisung You and Boram Cho propose HOMER, or Huber-of-Means for Efficient and Robust Estimation, which aggregates block means through a radial Huber center. Its canonical and pseudo-Huber forms bound each block score and interpolate between median-like robustness and the empirical mean. The work establishes a Hilbert-space majority theorem and a MOM-order deviation bound under a finite second moment. Canonical HOMER recovers the sample mean inside its quadratic region, while pseudo-HOMER approaches the sample mean as the threshold grows. Under a finite third moment, fixed finite-dimensional projections support mean inference at the usual parametric rate, though this requires growing block sizes and counts, with block sizes increasing faster. Heavy-tailed simulations show HOMER remains stable when a minority of block summaries is displaced, and on clean Gaussian data both versions closely approach the empirical mean's efficiency. Finite-block sandwich intervals undercovered, especially for skewed functional data, and further studies show failure when contamination affects most blocks or compromises ordinary within-block means.