Collaborative Research: Use of Random Compression Matrices For Scalable Inference in High Dimensional Structured Regressions

随着科学界进入数据驱动的时代，利用大规模成像、遗传和电子病历数据来更好地表征和了解人类疾病以改善治疗和预后的机会前所未有。因此，在过去十年中，用灵活的统计模型分析这些数据集已成为一个非常活跃的研究领域。为此，该项目计划开发一种全新的方法，该方法基于使用设计良好的机制压缩大数据获得的数据集上拟合统计模型的思想。该开发能够以前所未有的规模对大量数据进行高效建模。虽然研究人员的动机主要来自于对大量生物医学数据的复杂建模和不确定性量化，但统计方法的普遍性足以在机器学习和环境科学的相关文献中留下重要的足迹。总体目标还包括开发软件工具包，以便更好地为相关学科的从业者服务。此外，这些项目将为研究生和本科生，包括女性和少数民族社区的学生提供第一手培训机会，了解最先进的统计方法和成像/遗传/电子病历数据。通过将项目成果以学生能够理解的术语传播给他们，该项目将对提高公众对统计的科学素养产生深远的影响。在复杂和高维数据时代，现代统计学习方法的两个关键方面是准确性和推理规模。现代数据日益复杂化、高维化，涉及的变量数量多、样本量大，不同变量之间的关系复杂。开发实际有效（在存储和分析方面）和理论上“最优”的贝叶斯高维参数或非参数回归方法，从如此复杂的数据集中得出具有有效不确定性的准确推断是一个极其重要的问题。为了提供这个问题的一般解决方案，研究人员将开发基于使用少量随机线性变换的数据压缩的方法。该方法要么使用压缩减少与每个变量对应的大量记录，在这种情况下，它保持特征解释以进行充分的推理，要么使用压缩减少每个样本的协变量向量的维度，在这种情况下，重点只放在响应的预测上。在任何一种情况下，数据压缩都有助于在具有足够丰富的参数和非参数回归模型的高维数据中进行高效，可扩展和准确的贝叶斯推理/预测。一个重要的目标是建立关于压缩数据的拟合模型的收敛行为的精确理论结果，作为预测器数量、样本量、随机线性变换的性质和这些模型的特征的函数。这些方法将通过结合来自英国生物银行数据库的脑成像数据、遗传数据和电子健康记录（EHR）数据，用于研究神经系统疾病。该项目还将在更广泛的方面促进跨学科研究培训和扩大统计科学的参与。该奖项反映了美国国家科学基金会的法定使命，并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。

As the scientific community moves into a data-driven era, there is an unprecedented opportunity to leverage large scale imaging, genetic and EHR data to better characterize and understand human disease to improve treatment and prognosis. Consequently, analysis of such datasets with flexible statistical models has become an enormously active area of research over the last decade. To this end, this project plans to develop a completely new class of methods, which are based on the idea of fitting statistical models on datasets obtained by compressing big data using a well designed mechanism. The development enables efficient modeling of massive data on an unprecedented scale. While the motivation of the investigators comes primarily from complex modeling and uncertainty quantification of massive biomedical data, the statistical methods are general enough to set important footprints in the related literature of machine learning and environmental sciences. The overarching goal also includes the development of software toolkits to better serve practitioners in related disciplines. Further, the projects will provide first hand training opportunities for graduate and undergraduate students, including female and students from minority communities, in state-of-the-art statistical methodologies and imaging/genetic/EHR data. By disseminating the outcome of the project among high school students in terminology that they can understand, the project can have far reaching effects to enhance public scientific literacy about statistics.Two crucial aspects of modern statistical learning approaches in the era of complex and high dimensional data are accuracy and scale in inference. Modern data are increasingly complex and high dimensional, involving a large number of variables and large sample size, with complex relationships between different variables. Developing practically efficient (in terms of storage and analysis) and theoretically “optimal” Bayesian high dimensional parametric or nonparametric regression methods to draw accurate inference with valid uncertainties from such complex datasets is an extremely important problem. To offer a general solution for this problem, the investigators will develop approaches based on data compression using a small number of random linear transformations. The approach either reduces a large number of records corresponding to each variable using compression, in which case it maintains feature interpretation for adequate inference, or, reduces the dimension of the covariate vector for each sample using compression, in which case the focus is only on prediction of the response. In either case, data compression facilitates drawing storage efficient, scalable and accurate Bayesian inference/prediction in presence of high dimensional data with sufficiently rich parametric and nonparametric regression models. An important goal is to establish precise theoretical results on the convergence behavior of the fitted models with compressed data as a function of the number of predictors, sample size, properties of random linear transformations and features of these models. The approaches will be used to study neurological disorders by combining brain imaging data, genetic data and electronic health records (EHR) data from the UK Biobank database. The project will also contribute on a broader front to advancing the interdisciplinary research training and broadening participation in statistical sciences.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.