论文标题
禁止知识和专业培训：线性回归中过度拟合的两个主要来源的多功能解决方案
Forbidden Knowledge and Specialized Training: A Versatile Solution for the Two Main Sources of Overfitting in Linear Regression
论文作者
论文摘要
线性回归中的过度拟合被分解为两个主要原因。首先，估算器的公式包括有关培训观察结果的“禁止知识”，在部署样本外时会失去这一优势。其次，估算器具有“专业培训”，使其特别能够解释预测因子中对训练样本具有特质的运动。引入了样本外的培训观测值的“杠杆”量度的重要性。提出了一种新方法，以预测部署时的样本外拟合，当已知预测因子的值但实际结果变量却不是。在蒙特卡洛模拟和使用MRI脑扫描的经验应用中，所提出的估计量与平均样本外病例的预测剩余误差总和（按）相当，并且与按压不同，在不同的测试样品中也持续执行，甚至与训练集有很大不同的测试样品。
Overfitting in linear regression is broken down into two main causes. First, the formula for the estimator includes 'forbidden knowledge' about training observations' residuals, and it loses this advantage when deployed out-of-sample. Second, the estimator has 'specialized training' that makes it particularly capable of explaining movements in the predictors that are idiosyncratic to the training sample. An out-of-sample counterpart is introduced to the popular 'leverage' measure of training observations' importance. A new method is proposed to forecast out-of-sample fit at the time of deployment, when the values for the predictors are known but the true outcome variable is not. In Monte Carlo simulations and in an empirical application using MRI brain scans, the proposed estimator performs comparably to Predicted Residual Error Sum of Squares (PRESS) for the average out-of-sample case and unlike PRESS, also performs consistently across different test samples, even those that differ substantially from the training set.
