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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.

该项目将研究新的统计学习方法，用于解决需要解决空间邻近性以及数据中的物理，结构和时间约束的分组变量选择问题。例如，在遗传学研究中，通常已知同一遗传途径中的一组基因表现为一组;在神经科学应用中，大脑的空间连续区域通常表现为同质单元;在工业应用中，对于分类协变量，具有多个水平的因子通常被视为单个单元。该项目将设计基于数学优化的新的统计学习方法，为分组变量选择问题拓宽纪律统计和计算建模的范式。该研究还将涉及对研究生的指导以及与工业合作伙伴的合作。该项目将涉及课程编制和制作供公众使用的软件。该项目将探索基于混合整数优化的计算方法，以解决分组变量选择问题。虽然基于凸松弛的程序和贪婪方法在这个问题中发挥了重要作用，但混合整数优化方法的功能和通用性在很大程度上尚未开发。该项目将研究这一新方向，利用过去10到15年数学优化领域的进展。该项目的成功执行将创建新的工具，大大丰富了统计学家/机器学习者的工具包，这些工具包包含具有原则性计算和统计特性的可解释模型。该项目将研究通过使用先进的计算方法而不是常用的，计算友好的替代方法来提高统计性能的可能性。这项研究将探索新方法与现有方法的基本联系。研究探索将刺激机器学习，统计，运筹学，数学优化和应用领域的交叉活动。将为所提议的方法开发软件。