Collaborative Research: Unlocking Complex Heterogeneity in Large Spatial-Temporal Data with Scalable Quantile Learning

Advancements in modern technology have exponentially increased the availability and complexity of spatial and spatiotemporal data across various fields, presenting unique challenges and opportunities. This project aims to develop scalable and efficient quantile learning techniques to unlock valuable insights from large-scale, heterogeneous spatial-temporal data, overcoming limitations in handling dynamic patterns and spatial variations while accounting for uncertainty. These new analytical techniques will have wide-ranging applications, revolutionizing our understanding of spatial and temporal variations in critical areas. For example, they can help identify communities facing disproportionate risks from environmental hazards, health crises, or crime, enabling more targeted and effective interventions. By making these techniques widely accessible through public software releases, the project will empower researchers and policymakers to leverage vast amounts of spatial-temporal data and address pressing societal issues more effectively. The project will also contribute to STEM education by engaging both undergraduate and graduate students in hands-on learning and incorporating research findings into course development. The project will develop scalable and efficient quantile learning methodologies, algorithms, and theories to address challenges in analyzing large-scale spatial-temporal data through three main research aims. First, the investigators will introduce a flexible quantile spatial model framework that simultaneously captures spatial nonstationarity and heterogeneity via spatially varying coefficients. Second, they will develop a scalable distributed learning procedure using domain decomposition computing to efficiently handle large spatial datasets across complex domains, including a communication-efficient aggregation method for estimating constant coefficients to ensure optimal efficiency. Third, the research will expand analysis from 2D to 3D to tackle complex and heterogeneous dynamics of extremely large spatiotemporal data, introducing a class of quantile spatiotemporal models and developing a robust, scalable estimating procedure to meet substantial computational demands. These advancements will significantly impact multiple areas of statistics, including large-scale computing, inference, optimization, and nonparametric approximation theory. 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.