III: Small: A New Perspective on Grouped Variable Selection via Modern Optimization

III：小：通过现代优化进行分组变量选择的新视角

基本信息

批准号：
1718258
负责人：
Rahul Mazumder
金额：
$ 31.8万
依托单位：
Massachusetts Institute of Technology
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2022-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1718258&HistoricalAwards=false
关键词：
III Small New Perspective Grouped

项目摘要

This project will investigate new statistical learning methods for grouped variable selection problems that require addressing spatial proximity as well as physical, structural, and temporal constraints in data. For example, in genetic studies, it is often known that a group of genes in the same genetic pathway behaves as a group; in neuroscience applications, spatially contiguous regions of the brain often behave as homogeneous units; in industrial applications, with categorical covariates, a factor with multiple levels is often treated as a single unit. The project will design new statistical learning methods based on mathematical optimization that broadens the paradigm of disciplined statistical and computational modeling for grouped variable selection problems. The research will also involve mentoring of graduate students and collaborations with industrial partners. The project will involve curriculum development and the creation of software for public use. The project will explore computational methods based on mixed integer optimization to address the grouped variable selection problem. While convex relaxation based procedures and greedy methods have played a significant role in this problem, the power and versatility of mixed integer optimization methods have been largely unexplored. The project will investigate this new direction, leveraging the advances in this field of mathematical optimization over the past ten to fifteen years. Successful execution of this project will create new tools, significantly enriching a statistician/machine learner's toolkit of interpretable models with principled computational and statistical properties. The project will investigate possible gains in statistical performance by using advanced computational methods over popularly used, computationally friendlier alternatives. The research will explore fundamental connections of the new approaches with existing methods. The research quest will stimulate activity at the intersection of machine learning, statistics, operations research, mathematical optimization and the applied domains. Software will be developed for the methods proposed.

该项目将研究针对数据中的空间接近性以及数据中的物理，结构和时间约束的分组可变选择问题的新统计学习方法。例如，在遗传研究中，人们经常知道，同一遗传途径中的一组基因作为一个组的表现。在神经科学应用中，大脑的空间连续区域通常是同质单位。在工业应用中，具有分类协变量，具有多个级别的因素通常被视为一个单元。该项目将基于数学优化设计新的统计学习方法，该方法扩大了分组可变选择问题的纪律统计和计算模型的范例。该研究还将涉及指导研究生以及与工业伙伴的合作。该项目将涉及课程开发和为公共使用的软件创建。该项目将探索基于混合整数优化的计算方法，以解决分组的变量选择问题。尽管基于凸放松的程序和贪婪方法在此问题中起着重要作用，但混合整数优化方法的功能和多功能性在很大程度上没有探索。该项目将研究这个新的方向，利用过去十到十五年的数学优化领域的进步。该项目的成功执行将创建新的工具，并大大丰富具有具有原始计算和统计属性的可解释模型工具包。该项目将通过使用高级计算方法来调查统计性能的可能提高，而不是普遍使用的计算更友好的替代方案。该研究将通过现有方法探索新方法的基本联系。研究任务将在机器学习，统计，操作研究，数学优化和应用领域的交集中刺激活动。将为提出的方法开发软件。