Date of Award

Spring 1-1-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Statistics and Data Science

First Advisor

Spielman, Daniel

Abstract

Causal inference has been an important topic across many fields, such as computer science, statistics, econometrics, epidemiology, psychometrics, and political science, for decades. In this dissertation, we present methodological innovations in causal inference for three problems: estimation, testing, and decision making. In the first chapter, we provide an overview of this dissertation and introduce potential outcomes framework and confounded contextual bandit. In the second chapter, we describe a new design-based framework for drawing causal inference in randomized experiments. Causal effects in the framework are defined as linear functionals evaluated at potential outcome functions. Knowledge and assumptions about the potential outcome functions are encoded as function spaces. This makes the framework expressive, allowing experimenters to formulate and investigate a wide range of causal questions. We describe a class of estimators for estimands defined using the framework and investigate their properties. The construction of the estimators is based on the Riesz representation theorem. We provide necessary and sufficient conditions for unbiasedness and consistency. Finally, we provide conditions under which the estimators are asymptotically normal, and describe a conservative variance estimator to facilitate the construction of confidence intervals for the estimands. In the third chapter, we approach detecting the existence of interference by formalizing it as a hypothesis testing. We focus our analysis on the risk of the test, which is the worst type I + type II errors, and the minimax testing error, which is the lowest risk incurred by the optimal test. For the problem of testing between SUTVA and a linear-in-means model of network interference, we construct an explicit test to show that the risk approaches zero in large samples. On the other hand, we prove an impossibility result: the minimax testing error for testing between constant treatment effect and SUTVA is 1. This means that every test must have large type I error on some null or type II error on some alternative. In the final chapter, we study the offline contextual bandit problem, where we aim to acquire an optimal policy using observational data. However, this data usually contains two deficiencies: (i) some variables that confound actions are not observed, and (ii) missing observations exist in the collected data. Unobserved confounders lead to a confounding bias and missing observations cause bias and inefficiency problems. To overcome these challenges and learn the optimal policy from the observed dataset, we present a new algorithm called Causal-Adjusted Pessimistic (CAP) policy learning, which forms the reward function as the solution of an integral equation system, builds a confidence set, and greedily takes action with pessimism. With mild assumptions on the data, we develop an upper bound to the suboptimality of CAP for the offline contextual bandit problem.

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