Error Density-dependent Empirical Risk Minimization

Empirical Risk Minimization (ERM) with the squared loss has become one of the most popular principles for designing learning algorithms. However, the existing mean regression models under ERM usually suffer from poor generalization performance due to their sensitivity to atypical observations (e.g., outliers). For alleviating this sensitivity, some strategies have been proposed by utilizing the quantitative relationship of error values with different observations to form robust learning objectives. Instead of focusing on error values, this paper considers the error density to uncover the structure information of observations and proposes a new learning objective, called Error Density-dependent Empirical Risk Minimization (EDERM), for robust regression under complex data environments. Property characterizations and experimental analysis validate the robustness and competitiveness of the proposed EDERM-based learning models. The implemented codes can be found at https://github.com/zhangxuelincode/EDERM.