Dimension Reduction and Representation Learning for Improved Estimation of Causal Parameters

Abstract

High-dimensional observational data, including electronic health records and omics measurements, create substantial challenges for causal inference. The growing complexity of such data can hinder both estimation and interpretation. This dissertation focuses on heterogeneous treatment effects, individualized treatment regimes, and mediation analysis, and develops dimension-reduction and representation-learning methods tailored to their causal targets to facilitate inference. First, we propose a sufficient dimension-reduction method that directly targets treatment effect heterogeneity by identifying a low-dimensional linear subspace of the covariates. Combined with kernel-based covariate-balancing, this representation facilitates the estimation of optimal individualized treatment regimes through outcome-weighted learning in observational settings. Second, we develop an envelope-based dimension-reduction method for causal mediation analysis with high-dimensional mediators. The method identifies mediator variation associated with both the exposure and the outcome while separating variation unrelated to one or both components of the mediation pathway.Finally, we develop a nonlinear representation-learning method for conditional average treatment effect estimation. The proposed neural-network architecture promotes information sharing among the nuisance functions and the conditional average treatment effect function through shared latent representations. The proposed framework can accommodate complex structured and unstructured covariates, such as images. Together, these methods provide a framework for extracting causally relevant representations from complex, high-dimensional data, with the goal of improving the accuracy, interpretability, and applicability of causal inference methods in complex data settings.