Statistical miscellany: causality, networks, and bandits

Abstract

In this dissertation, we make methodological contributions in three separate areas. In Chapter 2, we introduce a new algorithm for learning high-dimensional causal networks from observational data. Our algorithm, which is a simple modification to the well-known PC-Algorithm, provides reductions in both computational and sample complexity, by leveraging properties of common random graph families. In Chapter 3, we develop a penalized regression framework to integrate known network structure into high-dimensional generalized linear models. Our framework is unique in that it considers two-way structured data, where networks connect both the features and the observation units. We also introduce a statistical inference procedure to provide valid confidence intervals and hypothesis tests. Finally, in Chapter 4, we present an improved estimator for counterfactual policy evaluation in contextual bandit problems. This method is based on classifier-based density ratio estimation, and displays state-of-the-art performance for continuous action spaces. We conclude with a discussion in Chapter 5, describing the limitations of the work, and avenues for future research.