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经过修改的交叉验证和引导调整的惩罚回归方法产生了更好的预测模型
Menelaos Pavlou1, Rumana Z Omar1, Gareth Ambler1
1Department of Statistical Science, UCL, London, UK.
Biometrical journal. Biometrische Zeitschrift
|June 26, 2024
概括
新的调整方法改善了风险预测的惩罚回归模型. 与标准交叉验证相比,修改和引导调整减少了过度收缩,并改善了校准斜率 (CS),提高了对最大概率估计 (MLE) 的预测准确性.
科学领域:
- 统计 统计 统计 统计
- 生物统计学 生物统计学
- 机器学习 机器学习
背景情况:
- 在风险预测模型中,最大概率估计 (MLE) 通常会导致过拟合,导致极端预测和差校准 (校准斜率<1).
- 像Ridge和Lasso这样的惩罚性回归方法通过缩小系数提供解决方案,但标准交叉验证调整可以过度缩小系数,导致高可变性和糟糕的校准,特别是在较小的样本大小的情况下.
研究的目的:
- 调查标准交叉验证对减少训练数据集的使用是否导致调整参数 () 的高估和处罚回归模型中的过度收缩.
- 提出和评估一种修改的交叉验证调整方法,该方法使用更大的伪开发数据集,以确保交叉验证培训数据集与原始开发样本大小相匹配.
主要方法:
- 开发了一种修改的交叉验证调整方法,通过从引导式衍生伪开发数据集中估计调整参数 ().
- 这种修改后的调整确保了交叉验证训练数据集与原始数据集大小相同,解决了对的潜在高估.
- 修改调整和引导调整的性能与各种样本大小的模拟和真实数据集中的Ridge和Lasso回归的标准调整进行了比较.
主要成果:
- 与标准调相比,修改和引导调方法大大改善了调参数 () 的选择.
- 这些改进的调整方法导致了较好的校准斜率 (CS) 和较低的预测误差,相比标准调整.
- 在预测准确性方面,修改和引导调整都表现出比最大概率估计 (MLE) 更好的性能.
结论:
- 拟议的修改交叉验证调整方法有效地解决了与处罚回归模型相关的过度收缩和校准问题.
- 修改和引导调整为风险预测模型提供了更高的可靠性和准确性,特别是在样本规模有限或中等的场景中.
- 这些方法在标准的统计软件中很容易实现,为开发可靠的风险预测模型提供了实际增强.
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