[2603.25466] Residual-as-Teacher: Mitigating Bias Propagation in Student--Teacher Estimation

Statistics > Machine Learning arXiv:2603.25466 (stat) [Submitted on 26 Mar 2026] Title:Residual-as-Teacher: Mitigating Bias Propagation in Student--Teacher Estimation Authors:Kakei Yamamoto, Martin J. Wainwright View a PDF of the paper titled Residual-as-Teacher: Mitigating Bias Propagation in Student--Teacher Estimation, by Kakei Yamamoto and Martin J. Wainwright View PDF HTML (experimental) Abstract:We study statistical estimation in a student--teacher setting, where predictions from a pre-trained teacher are used to guide a student model. A standard approach is to train the student to directly match the teacher's outputs, which we refer to as student soft matching (SM). This approach directly propagates any systematic bias or mis-specification present in the teacher, thereby degrading the student's predictions. We propose and analyze an alternative scheme, known as residual-as-teacher (RaT), in which the teacher is used to estimate residuals in the student's predictions. Our analysis shows how the student can thereby emulate a proximal gradient scheme for solving an oracle optimization problem, and this provably reduces the effect of teacher bias. For general student--teacher pairs, we establish non-asymptotic excess risk bounds for any RaT fixed point, along with convergence guarantees for the student-teacher iterative scheme. For kernel-based student--teacher pairs, we prove a sharp separation: the RaT method achieves the minimax-optimal rate, while the SM method incu...