Robust low-rank tensor regression via truncation and adaptive Huber loss

Abstract

This paper investigates robust low-rank tensor regression with only finite (1 + ǫ)-th moment noise based on the generalized tensor estimation framework proposed by Han et al. ( 2022) [4]. The theoretical result shows that when ǫ ≥ 1, the robust estimator possesses the minimax optimal rate. While 1 > ǫ > 0, the rate is slower than the deviation bound of sub-Gaussian tails.