推导出岭回归在大数据下的最优训练测试集划分比例。
Test Set Sizing for the Ridge Regression
- 基于大样本极限推导出岭回归的最优数据分割方式。
- 结果表明分割比例主要依赖样本数和特征数，与正则化参数关系弱。
- 首次对机器学习模型在大数据下给出数学化的测试集划分方案。
本文在训练样本量 m 趋于无穷大的极限下，高精度推导出岭回归的理想训练/测试集划分比例。尽管该划分理论上应依赖于正则化参数 alpha，但研究发现其影响极弱，可忽略不计；最终仅剩样本数 m 与固定特征数 n 影响划分。这是首次在大数据极限下对机器学习模型进行数学化测试集划分推导。目标是最大化模型评估的“完整性”，使实测误差尽可能接近理论预期值。本文所得岭回归划分结果，与经典线性回归的已有成果在前两项渐近意义上完全一致。
原文摘要 · Abstract (English)
We derive the ideal train/test split for the ridge regression to high accuracy in the limit that the number of training rows m becomes large. The split must depend on the ridge tuning parameter, alpha, but we find that the dependence is weak and can asymptotically be ignored; all parameters vanish except for m and the number of features, n, which is held constant. This is the first time that such a split is calculated mathematically for a machine learning model in the large data limit. The goal of the calculations is to maximize "integrity," so that the measured error in the trained model is as close as possible to what it theoretically should be. This paper's result for the ridge regression split matches prior art for the plain vanilla linear regression split to the first two terms asymptotically.
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