标题： 模型选择中的拓扑技术 显示英文标题

标题： Topological Techniques in Model Selection

摘要： LASSO 是一种吸引人的线性回归正则化方法，它结合了变量选择与高效的计算过程。 本文致力于增强 LASSO 在无平方层次多项式模型中的性能，当结合验证误差与模型复杂度的度量时尤其如此。 复杂度的度量是将模型视为单纯复形时其 Betti 数的总和，我们借用计算拓扑学的最新发展，以成分和循环的方式描述该模型。 我们研究并提出了一种结合统计和拓扑标准的算法。 这种复合标准将使我们能够处理包含高阶交互作用的多项式回归模型中的模型选择问题。 模拟结果显示，复合标准产生的模型比其他几种统计方法对于高阶交互作用模型的估计器具有更稀疏的模型和更低的预测误差。 显示英文摘要

摘要： The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical polynomial models when combining validation error with a measure of model complexity. The measure of the complexity is the sum of Betti numbers of the model which is seen as a simplicial complex, and we describe the model in terms of components and cycles, borrowing from recent developments in computational topology. We study and propose an algorithm which combines statistical and topological criteria. This compound criterion would allow us to deal with model selection problems in polynomial regression models containing higher-order interactions. Simulation results demonstrate that the compound criteria produce sparser models with lower prediction errors than the estimators of several other statistical methods for higher order interaction models.