Doubly-robust variable selection in high dimensions

该项目将改进变量选择问题的方法。目标是选择哪些解释变量与感兴趣的结果变量相关。变量选择是一个基本的统计学问题，出现在无数的应用领域：哪些基因影响给定的人类疾病的流行？哪些人口统计学和社会经济学变量会影响一个人的收入？哪些电子健康记录条目会影响未来的医疗费用？特别是当潜在的解释变量的数量很大时，很难将重要的变量（信号）与不相关的变量（噪声）分开。变量选择问题在计算上也具有挑战性。这两个问题都阻碍了研究人员快速可靠地分析数据。该项目将通过开发几种方法创新并在开源软件包中分发由此产生的改进方法来应对这些重要挑战。该项目还将为研究生提供多种培训机会，让他们参与跨学科的研究活动。大量的研究已经进入高维变量选择问题和相关的条件独立性（CI）检验问题，包括模型X（MX）推理，去偏套索推理，双回归CI检验和半参数/因果推理。在CI测试问题的背景下（即评估单个变量是否与其他变量的响应相关的问题），研究人员最近领导了一项努力，以打破现有工作不同路线之间的障碍。从CI测试问题转移到变量选择问题，该项目将开发一种方法，满足一套详尽的具体统计和计算要求，所有这些要求都不能满足任何现有的方法。首先，该项目将开发一个程序来构建CI测试的零分布，这些测试在小样本中是准确的（如MX条件随机化测试），但只需要有限数量的重新采样（速度与双重回归方法相当）。其次，该项目将开发一种变量选择方法，该方法只需要一个机器学习步骤（如MX仿制品），但具有双重鲁棒性（如双重回归方法）。第三，开发并综合评价结合了上述两项创新的世界最佳变量选择方法--双重稳健变量选择（DRVS）。该奖项体现了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The project will develop improved methodologies for the variable selection problem. The goal is to choose which explanatory variables are associated with an outcome variable of interest. Variable selection is a fundamental statistical problem that arises in countless application areas: Which genes influence the prevalence of a given human disease? Which demographic and socioeconomic variables influence a person’s income? Which electronic health record entries influence future medical costs? Especially when the number of potential explanatory variables is large, it is difficult to separate the important variables (the signal) from the irrelevant ones (the noise). The variable selection problem is also computationally challenging. Both of these issues hamper the progress of researchers in analyzing their data quickly and reliably. The project will address these important challenges by developing several methodological innovations and distributing the resulting improved methods in an open-source software package. The project will also provide multiple training opportunities to graduate students by involving them in the interdisciplinary research activities.A wealth of research has gone into the high dimensional variable selection problem and the associated conditional independence (CI) testing problem, including model-X (MX) inference, debiased lasso inference, double regression CI testing, and semiparametric/causal inference. In the context of the CI testing problem (i.e. the problem of assessing whether a single variable is associated with the response given the others), the investigator has recently led an effort to break down the barriers between the distinct lines of existing work. Moving from the CI testing problem to the variable selection problem, the project will develop a methodology satisfying an exhaustive set of concrete statistical and computational requirements, all of which are not met by any existing methodology. First, the project will develop a procedure to construct null distributions for CI tests that are accurate in small samples (like the MX conditional randomization test) but require only a limited number of resamples (giving speed comparable to that of double regression approaches). Second, the project will develop a variable selection method that requires only a single machine learning step (like MX knockoffs) but is doubly robust (like double regression methods). Third, the project will develop and comprehensively evaluate Doubly Robust Variable Selection (DRVS), a best-of-all-worlds variable selection methodology incorporating the above two innovations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.