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

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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.