Nonlinear Monte Carlo Method for Imbalanced Data Learning
This addresses robustness and generalization issues in imbalanced data problems for machine learning applications, representing an incremental improvement.
The paper tackles the problem of overfitting and poor generalization in imbalanced data learning by proposing a nonlinear Monte Carlo method that replaces the mean loss with the maximum subgroup mean loss, achieving better performance and robustness than SOTA models with fewer training steps.
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed (i.i.d.) and the mean value of loss function is used as the empirical risk by Law of Large Numbers (LLN). This is known as the Monte Carlo method. However, when LLN is not applicable, such as imbalanced data problems, empirical risk will cause overfitting and might decrease robustness and generalization ability. Inspired by the framework of nonlinear expectation theory, we substitute the mean value of loss function with the maximum value of subgroup mean loss. We call it nonlinear Monte Carlo method. In order to use numerical method of optimization, we linearize and smooth the functional of maximum empirical risk and get the descent direction via quadratic programming. With the proposed method, we achieve better performance than SOTA backbone models with less training steps, and more robustness for basic regression and imbalanced classification tasks.