Collaborative Research: Design-Based Optimal Subdata Selection Using Mixture-of-Experts Models to Account for Big Data Heterogeneity

随着技术的进步，为大多数研究领域收集大量数据变得很容易。但由于数据集的大小以TB甚至PB为单位测量，分析此类数据集可能会成为一项昂贵的计算挑战，在典型的台式机或笔记本电脑上可能是不可能的。然而，为了做出有影响力的发现，可能没有必要分析整个数据集。因此，人们对开发和研究从海量数据集中选择子集并基于小得多的所选数据集得出结论的方法非常感兴趣。这种方法称为子数据选择或子抽样方法。一种明显的二次抽样方法是从整个数据集中随机选择数据。虽然这通常是最简单和最快的选择，但已经确定，更好的选择通常是可用的。在这个项目中，首席调查者(PI)的目标是开发和研究一个严格的框架和新的方法，通过使用考虑到数据中的异质性的模型来优化子数据选择，这种异质性通常存在于大型数据集中。研究成果将被纳入专题课程，以培训研究生进行大规模数据分析。这项工作也将通过PIS在公共卫生、生物医学和商业方面的合作来传播。PIS计划开发和研究基于混合专家(ME)模型的子数据选择方法，该方法可以解释数据中的异质性，而不是假设多元回归模型。PI最初将开发和研究ME模型的一个子类的子数据选择方法，称为簇式线性回归模型，对于这种模型，门函数是常量。接下来将研究Logistic-正态混合模型，其中门函数依赖于回归变量。对于这两种情况，调查人员计划开发基于信息的最佳子数据选择方法，首先针对连续响应变量，然后针对二元响应变量，研究其统计特性，并为将在R包中提供的方法开发高效算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

With technological advances, it has become easy to collect massive amounts of data for most areas of research. But with the size of datasets measured in terabytes or even petabytes, analyzing such datasets can become an expensive computational challenge and may be impossible on a typical desktop or laptop computer. However, for making impactful discoveries, it may be unnecessary to analyze an entire dataset. Consequently, there is great interest in developing and studying methods for selecting a subset from a massive dataset and for drawing conclusions based on the much smaller selected dataset. Such methods are known as subdata selection or subsampling methods. One obvious subsampling method consists of randomly selecting data from the entire dataset. While this is often the simplest and fastest option, it has been established that better options are often available. In this project, the principal investigators (PIs) aim to develop and study a rigorous framework and new methods for optimal subdata selection by using models that account for heterogeneity in the data, which is often present in large datasets. Research findings will be incorporated in topical courses to train graduate students in large-scale data analysis. The work will also be disseminated via the PIs’ collaborations in public health, biomedical science, and business.Rather than assuming a multiple regression model, the PIs plan to develop and study subdata selection methods based on mixture-of-experts (ME) models, which can account for heterogeneity in the data. The PIs will initially develop and study subdata selection methods for a subclass of the ME models, known as clusterwise linear regression models, for which the gate functions are constant. This will be followed by studying logistic-normal mixture models, in which the gate functions depend on the regression variables. For both cases, the investigators plan to develop information-based optimal subdata selection methods, first for continuous response variables and then for binary response variables, study their statistical properties, and develop efficient algorithms for the methods that will be made available in an R package.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.