Statistical Machine Learning for Spatial- and Network-Linked Data

Abstract

Statistical machine learning techniques offer versatile tools for prediction, estimation and inference across a wide range of applications. However, the ability of existing methods to handle data with dependence induced by complex spatial or network structures is limited, despite the increasing potential of such data due to recent advances in data collection technologies. This dissertation develops statistical machine learning methodologies that are well suited for such settings and require weaker assumptions than many existing alternatives. We start our discussion with an intuitive variable importance measure for a broad class of black-box spatial prediction models in Chapter 2. We then introduce a flexible dimensional reduction algorithm for spatial data in Chapter 3, which leads to superior performance in downstream modeling tasks while preserving approximation accuracy. In Chapter 4, we propose a computationally efficient estimation and inference procedure for doubly-stochastic spatial point processes that does not rely on certain common but stringent model assumptions. In Chapter 5, we investigate estimation and inference for direct and indirect causal effects of treatments in imperfectly randomized trails, with the presence of cross-unit interference on random graphs.