High-Dimensional Nonstationary Processes for Spatial Analysis and Machine Learning

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Numerous application problems in geosciences, climate and environmental sciences, public health, social sciences and traffic statistics involve large amounts of spatial data collected from complex constrained domains with non-trivial geometries, such as irregular boundaries with sharp concavities, interior holes due to geographic constraints, and river or road networks. Practitioners are interested in modeling complex spatial dependence because it plays the most important role in the estimation and prediction of spatial problems. However, there is very limited tool for the estimation and prediction of spatial problems on complex domains. This project aims to develop new statistical models and algorithms to better characterize the potentially much more heterogeneous spatial dependence in large data sets while respecting irregular geometries in the data. The methodology will be applicable to a broad range of real problems in multiple interdisciplinary fields. The proposed research initiatives will offer numerous opportunities for interdisciplinary research training at undergraduate and graduate levels, with a particular focus on advancing diversity and inclusion in statistical sciences.This project will introduce a new class of nonstationary models with flexible locally stationary dependence structures for large spatial data. The detection of locally stationary structures is achieved by a novel manifold partition model with flexible partition boundaries while respecting irregular shapes of domain boundaries. The project will further develop a novel framework to build a valid stochastic process model to knit together local models. Both parameter estimation and prediction can be performed under a unified framework, and both discontinuities/abrupt changes and smoothness in spatial random field can be captured. Moreover, the project will result in new scalable and parallelizable divide-merge-conquer inference tools, harnessing the power of locally stationary assumptions. The performance of the proposed methods will be tested with simulation studies and applied to real-life applications.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.