论文标题
非线性蒙特卡洛方法用于数据不平衡的数据学习
Nonlinear Monte Carlo Method for Imbalanced Data Learning
论文作者
论文摘要
对于基本的机器学习问题，预期错误用于评估模型性能。由于数据的分布通常是未知的，因此我们可以简单地假设数据是独立和相同分布的数据（i.i.d.），并且损失函数的平均值被大量定律（LLN）用作经验风险。这被称为蒙特卡洛法。但是，当不适用LLN（例如数据问题）等LLN时，经验风险将导致过度拟合，并可能降低鲁棒性和泛化能力。受非线性期望理论框架的启发，我们将损失函数的平均值代替亚组平均损失的最大值。我们称其为非线性蒙特卡洛法。为了使用优化的数值方法，我们将最大经验风险的功能线性化并平滑，并通过二次编程获得下降方向。通过提出的方法，我们比SOTA主干模型获得了更好的训练步骤，并且对于基本回归和分类任务的鲁棒性更高。
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.
