Beyond Least Squares: Robust Regression Transformer (R2T)
This addresses robust regression for data with asymmetric noise, such as in wearable applications, but is incremental as it builds on hybrid neural-symbolic approaches.
The paper tackles the problem of robust regression failing with asymmetric structured noise by proposing a hybrid neural-symbolic architecture, achieving a median regression MSE of 6e-6 to 3.5e-5, which is a 10-300 times improvement over existing methods like ordinary least squares and Huber loss.
Robust regression techniques rely on least-squares optimization, which works well for Gaussian noise but fails in the presence of asymmetric structured noise. We propose a hybrid neural-symbolic architecture where a transformer encoder processes numerical sequences, a compression NN predicts symbolic parameters, and a fixed symbolic equation reconstructs the original sequence. Using synthetic data, the training objective is to recover the original sequence after adding asymmetric structured noise, effectively learning a symbolic fit guided by neural parameter estimation. Our model achieves a median regression MSE of 6e-6 to 3.5e-5 on synthetic wearable data, which is a 10-300 times improvement when compared with ordinary least squares fit and robust regression techniques such as Huber loss or SoftL1.