Integrative Analysis on Heterogeneous Datasets with High-Dimensional and Non-Standard Models

在过去十年中，数据收集技术的进步使从业者能够收集关于许多自然和社会现象的更大和更全面的数据集。尽管这一趋势使从业者能够获得新的见解，但它也带来了一些警告，如果不加以解决，可能会导致错误的结论，而这些结论正是某些科学领域可重复性危机的核心。注意事项包括：(i)现代数据集的异质性日益增强，这不仅是世界上固有的多样性的结果，也是将来自多个来源的数据组合起来创建更全面数据集的趋势。不适当地考虑这种日益增长的异质性可能导致从业者系统性地得出有偏见的结论。（ii）现代数据集的规模阻碍了从中得出推论。将一个标准模型拟合到一个庞大的数据集在计算上是难以处理的。（iii）现代数据集的综合性引发了隐私和安全问题。综合分析可能会发现多个来源的模式组合，这些模式单独无害，但共同识别，从而加剧了这种情况。首席研究员的目标是通过设计通信避免方法来解决异构数据集集成分析中出现的异质性、大小和隐私/安全问题。在高层次上，一般的方法是用本地计算代替通信：计算每个数据源的有损摘要，并对摘要执行综合分析。通过这种方式，只组装摘要，从而降低了通信成本，并保持了独立数据源的匿名性和安全性。PI工作的具体目标包括(i)在具有可证明的统计保证的流行高维模型中异构分布式计算的有效计算策略，以及（ii）对“不可微”统计问题的数据集成的新方法和理论见解，其中通过在凸锥的边界上投影或通过优化不连续准则函数来获得估计量。并且在现代研究领域中越来越多地出现。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。

Advances in data collection technology in the past decade have enabled practitioners to collect larger and more comprehensive datasets about many natural and social phenomena. Although this trend has enabled practitioners to gain new insights, it also comes with caveats that, if not addressed, may lead to erroneous conclusions that lie at the core of the reproducibility crisis in some areas of science. The caveats include: (i) Modern datasets are growing in heterogeneity, not only as a consequence of the inherent diversity in the world, but also the trend of combining data from multiple sources to create more comprehensive datasets. Not properly accounting for this growing heterogeneity may lead practitioners to systematically biased conclusions. (ii) The size of modern datasets is a hindrance to drawing inferences from them. Fitting a standard model to a massive dataset can be computationally intractable. (iii) The comprehensive nature of modern datasets raises privacy and security concerns. This is exacerbated by integrative analysis that may uncover combinations of patterns in multiple sources that are individually innocuous, but jointly identifying.The Principal Investigator aims to address the heterogeneity, size, and privacy/security concerns that arise in integrative analysis of heterogeneous datasets by designing communication avoiding methods. At a high level, the general approach is to trade local computation for communication: compute lossy summaries of each data source and perform integrative analysis on the summaries. This way, only the summaries are assembled, thereby reducing the communication costs and preserving the anonymity and security of the separate data sources. The specific aims of the PI's work include (i) effective computational strategies for distributed computing under heterogeneity in popular high-dimensional models with provable statistical guarantees, and (ii) new methodological and theoretical insights into data integration for "non-differentiable" statistical problems in which estimators are obtained by projecting either on the boundaries of a convex cone or via the optimization of discontinuous criterion functions, and which arise increasingly in modern domains of research.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.