Collaborative Research: Generative Bootstrapping Methods for Massive Dependent Data

This project advances the statistical foundations for reliable inference from massive dependent data (e.g., spatial and spatiotemporal data). Such data naturally arise in many applications, including transportation systems, healthcare, manufacturing, remote sensing, and digital twins. Standard tools for constructing large-sample confidence intervals or prediction intervals are often computationally expensive, difficult to scale, and/or inaccurate when applied to large dependent data. To address these challenges, the investigators will combine approximate inference for dependent data with tools from modern generative artificial intelligence (AI) to enable faster, more reliable, and more scalable uncertainty assessment. This will help support trustworthy decision-making in data-intensive fields. This project will also create new open-access educational materials, support outreach and research opportunities for students of all levels, produce publicly available software, and train undergraduate and graduate students in modern statistics, data science, and AI. The main thrust of this project is to introduce a computationally efficient generative bootstrapping framework for approximate inference with massive dependent data. Exact inference is often infeasible in the presence of large-scale dependence. In contrast, approximate likelihood methods such as the Vecchia approximation and composite likelihood allow for computationally tractable inference by replacing the exact joint likelihood with a surrogate made from low-dimensional marginal or conditional distributions of subsets. Uncertainty quantification for approximate likelihoods can be performed using re/sampling procedures such as bootstrapping. However, traditional bootstrapping requires repeated resampling and re-estimation, greatly limiting its feasibility for large dependent data, especially on resource-constrained hardware. To overcome this bottleneck, this project integrates deep generative models with bootstrap resampling to allow for single-pass inference under Vecchia approximations and composite likelihoods. The key idea is to use deep neural networks to learn a deterministic mapping from random bootstrap weights, data subsets, and tuning parameters to an implicit bootstrap distribution. Once this mapping is learned in a single optimization, the cost of generating samples from the bootstrap distribution is negligible. The investigators will establish the asymptotic validity of these generative bootstrap samplers, including higher-order accuracy for iterative bootstrap procedures. In doing so, this project pioneers a theoretically grounded framework for scalable uncertainty quantification of massive dependent data. 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.