Bias Term for Outlier Detection and Robust Regression

Noisy data and outliers are among the main challenges in machine learning, as their presence in training data can significantly reduce model performance and generalization. Detecting and handling these anomalous samples is particularly difficult because it is hard to distinguish them from normal data. In this study, we propose a novel bias-based method (BT-SVR) to detect outliers and noisy inputs. The method uses a bias term derived from pairwise relationships among data points, which captures structural information about input distances. Outliers and noisy samples typically produce near-zero bias responses, allowing them to be identified effectively. A root-mean-square (RMS) scoring mechanism is then applied to quantify the anomaly strength of each sample, enabling the impact of outliers to be underweighted before training. Experiments demonstrate that BT-SVR improves the performance of Support Vector Regression (SVR) and enhances its robustness against noisy and anomalous data.