Learning subgroups from data: selective inference and applications

像聚类和回归树这样的“子组学习”方法被用来将大型、复杂的数据集分成尽可能同质的小块（“子组”）。这些方法已经被用于一些重要的任务，比如识别对实验性药物有不同反应的患者亚组，识别具有不同生物学特征的肿瘤亚组（导致有针对性的治疗策略），以及识别可能更有可能购买特定产品的客户（导致有针对性的广告策略）。在这个提案中，我概述了我的计划，以开发新的统计方法来确定数据集中确定的子组是否真正不同，并应用子组学习来解决称为空间填充设计领域的难题。一旦我们确定了数据集中的子组，很自然地想知道它们是否真的不同。毕竟，如果子组学习方法识别出具有相同生物学特征的肿瘤子组，或者具有相同购买偏好的客户子组，那么针对这些子组进行靶向治疗或广告策略将是对时间和资源的巨大浪费。不幸的是，现有的用于检验两组是否不同的经典统计方法过于乐观，并且几乎总是会声称子组不同，因为它们没有考虑到数据的双重使用：一次确定候选子组，再次确定它们是否不同。为了解决这个问题，研究计划提出了统计方法，在测试使用聚类和回归树确定的子组之间的均值差异时，适当地考虑数据的双重使用。我将进一步强调子组学习方法在称为空间填充设计的统计领域中尚未开发的潜力，其目的是在整个空间中均匀分布点。这些设计被广泛应用于计算机实验中，这些实验使用计算机模型来模拟输入变量对天气和海冰等物理系统的影响。空间填充设计也用于设计环境监测网络，如空气质量和水声监测网络。虽然空间在实践中往往是复杂的（例如海岸线上的网络），但除非空间很简单，否则很难构建空间填充设计。我提出了一种基于应用子群学习方法（层次聚类）的策略，可以在任意复杂的空间上构建空间填充设计。在这个研究项目中，研究生和本科生将为产生影响生物学和公共卫生等领域的科学进步速度的统计方法做出贡献，并成为小组学习的专家，这将是他们未来在学术界和工业界作为统计学家或数据科学家的宝贵财富。

"Subgroup learning" methods like clustering and regression trees are used to split large, complex data sets into smaller chunks ("subgroups") that are as homogeneous as possible. These methods have been used for important tasks like identifying subgroups of patients that respond differently to an experimental drug, identifying subgroups of tumours that have different biological profiles (leading to targeted treatment strategies), and identifying customers who might be more likely to purchase particular products (leading to targeted advertising strategies). In this proposal, I outline my plans to develop new statistical methodology to determine if identified subgroups in a data set are truly different, and to apply subgroup learning to solve a difficult problem in an area called space-filling designs.  Once we have identified subgroups in a data set, it is natural to want to know whether they are truly different. After all, if the subgroup learning method identified subgroups of tumours that all have the same biological profiles, or subgroups of customers who all have the same purchasing preferences, it would be a massive waste of time and resources to target treatment or advertising strategies to these subgroups. Unfortunately, existing classical statistical methods for testing whether two groups are different are overly optimistic and will almost always claim that the subgroups are different, because they do not account for the double use of the data: once to identify candidate subgroups, and once again to determine whether they are different. To solve this problem, the research program proposes statistical methods that properly account for the double use of the data, when testing for differences in means between subgroups identified using clustering and regression trees.  I will further highlight the untapped potential of subgroup learning methods in a statistical area called space-filling designs, which aims to evenly distribute points throughout a space. These designs are widely used in computer experiments, which use computer models to simulate the effect of input variables on physical systems like weather and sea ice. Space-filling designs are also used to design environmental monitoring networks, like air quality and underwater acoustic monitoring networks. Although spaces are often complex in practice (e.g. networks on coastlines), it is difficult to construct space-filling designs unless the space is simple. I propose a strategy based on an application of a subgroup learning method (hierarchical clustering) that can construct space-filling designs on arbitrarily complex spaces.  In this research program, graduate and undergraduate students will contribute to producing statistical methods that impact the rate of scientific advancement in areas like biology and public health, and become experts in subgroup learning, which will be a valuable asset to their future careers as statisticians or data scientists in academia and industry.