论文标题
分层多项式模型的套索
Lasso for hierarchical polynomial models
论文作者
论文摘要
在多项式回归模型中，多项式层次结构中隐含的划分条件让位于模型参数的自然结构。我们使用此原理来得出强大和弱的层次结构的版本，并扩展文献中的现有作品，目前仅与第二学位的模型有关。我们讨论了如何使用标准二次编程技术估算套索中的参数，并将我们的建议应用于文献中的模拟数据和示例。所提出的方法在低验证误差和模型大小方面与现有技术相比有利。
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy and to extend existing work in the literature, which at the moment is only concerned with models of degree two. We discuss how to estimate parameters in lasso using standard quadratic programming techniques and apply our proposal to both simulated data and examples from the literature. The proposed methodology compares favorably with existing techniques in terms of low validation error and model size.
