Speaker: Arjun Sondhi, Graduate Student, UW Biostatistics
Abstract: This dissertation consists of three tenuously related parts. In the first part, we develop an efficient algorithm for learning the causal network connecting a large set of variables. Our proposed method offers significant gains in computational complexity and estimation accuracy, particularly for graphs with hub nodes. The theory for our algorithm results from directly incorporating properties of common random graph families. The second part focuses on binary data regression subject to network information. We develop estimation and inference for a penalized regression that accounts for known networks among both the predictors and the observation units. Specifically, we provide results for a correlated probit model with a network penalty, by extending previous high-dimensional inference work. The final part of the dissertation develops a method for counterfactual policy evaluation in contextual bandit and reinforcement learning settings with continuous action spaces. Most existing methods focus on discrete or parametric actions spaces with known densities. Our method directly estimates a density ratio through probabilistic classification, and requires no knowledge of either density, nor does it make any assumptions on the density shapes.