Residual-as-Teacher: Mitigating Bias Propagation in Student--Teacher Estimation
This addresses bias mitigation in machine learning models for researchers and practitioners, offering a novel approach with theoretical guarantees, though it is incremental as it builds on existing student-teacher frameworks.
The paper tackles the problem of bias propagation in student-teacher estimation by proposing the Residual-as-Teacher (RaT) method, which reduces teacher bias effects and achieves minimax-optimal rates in kernel-based settings, while experiments show improved performance under covariate shift.
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 incurs constant prediction error for any sample size. Experiments on both synthetic data and ImageNette classification under covariate shift corroborate our theoretical findings.