Variable Selection via Inverse Modeling for Detecting Nonlinear Relationships

通过逆向建模进行变量选择以检测非线性关系

• 批准号: 1613035
• 负责人: Jun Liu
• 金额: $ 20万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1613035&HistoricalAwards=false
• 关键词: Variable; Selection; via; Inverse; Modeling

With the ever-growing amount of data in many application areas, effective methods for detecting factors influencing the value of a response variable are in high demand. It is of growing importance to develop methods for detecting variables that exert significant nonlinear response. Inspired by the sliced inverse regression method developed in the early 1990s, the PI proposes a general framework for developing effective variable selection strategies in nonlinear systems of high dimension. The PI will further study theoretical properties of these variable selection algorithms. The proposed theoretical investigation will provide theoretical understanding of limitations of existing dimension-reduction techniques when the dimensionality grows with the sample size. With the ever-growing amount of data in many application areas, effective methods for detecting factors that may influence the value of a target quantity of interest (response variable) are in high demand. The problem is termed as "variable (or feature) selection" in regression modeling and statistical learning, and is a long-standing problem in statistics and machine learning. The PI focuses here on the detection of factors that may exert nonlinear and/or interactive effects on the response variable. Recent studies from the PI's group reveal that the sliced inverse regression (SIR) and inverse modeling strategies provide a powerful framework for developing effective variable selection strategies in nonlinear systems of high dimension. The PI aims at developing more robust and effective tools for detecting such complex relationships and studying theoretical properties of SIR-based algorithms. The proposed method will also be applicable to do robust variable selection for classification problems. The proposed theoretical investigations will provide (a) theoretical understanding of limitations of existing dimension-reduction techniques when the dimensionality grows with the sample size; (b) guidance on the construction of necessary sparsity conditions that can guarantee consistency of variable selections in ultra-high dimensional nonlinear problems; (c) the optimal convergence rate of that the best possible learning algorithm can achieve in such settings; and (d) theoretical justifications whether the proposed algorithms can achieve or are not far from the optimality.

随着许多应用领域中数据的不断增长，检测影响响应变量价值的因素的有效方法很高。开发用于检测具有显着非线性反应的变量的方法越来越重要。受到1990年代初期开发的切片反回归方法的启发，PI提出了一个通用框架，用于在高维的非线性系统中制定有效的可变选择策略。 PI将进一步研究这些可变选择算法的理论特性。提出的理论研究将在尺寸随样本量增长时对现有尺寸还原技术的局限性提供理论上的理解。 随着许多应用领域中数据的不断增长，检测可能影响目标量数量（响应变量）价值的因素的有效方法在很高的需求中。该问题在回归建模和统计学习中被称为“变量（或功能）选择”，并且是统计和机器学习中的长期问题。 PI在这里重点是检测可能对响应变量发挥非线性和/或交互作用的因素。 PI小组的最新研究表明，切成薄片的反回归（SIR）和反向建模策略为在高尺寸的非线性系统中制定有效的可变选择策略提供了有力的框架。 PI旨在开发更健壮和有效的工具来检测这种复杂的关系并研究基于SIR算法的理论特性。所提出的方法也将适用于对分类问题进行健壮的变量选择。提出的理论研究将提供（a）当维度随样本量增长时，对现有尺寸还原技术的局限性的理论理解； （b）关于构建必要的稀疏条件的指导，这些条件可以保证超高维非线性问题中可变选择的一致性； （c）最好的学习算法可以在这种情况下实现的最佳收敛率； （d）理论上的理由是拟议的算法可以实现还是距离最佳性不远。

项目成果

On the optimality of sliced inverse regression in high dimensions

• DOI: 10.1214/19-aos1813
• 发表时间: 2017-01
• 期刊: The Annals of Statistics
• 作者: Q. Lin;Xinran Li;Dongming Huang;Jun S. Liu