Estimation and Inference in Causal Models and Multi-Modal Knowledge Graph Integration

Abstract

This dissertation examines the estimation and inference of causal parameters in two different frameworks: the generalized method of moments framework and the dynamic optimal treatment regime framework.

For generalized method of moments framework: Chapter 1 shows that when the auxiliary estimators satisfy a leave-one-out stability condition, debiased machine learning can achieve root-n consistency and asymptotic normality without requiring sample splitting or cross-fitting. This enables more efficient sample reuse, especially in moderate-sample regimes.

For dynamic optimal treatment regimes: Chapter 2 analyzes the statistical properties of a softmax approximation to the optimal policy. It demonstrates that under a suitable growing scheme of the temperature parameter, this softmax approach yields valid inference for the value and structural parameters associated with the true optimal regime.

Apart from causal parameter estimation and inference, this dissertation also advances causal understanding by integrating biomedical knowledge to uncover biological drivers of clinical outcomes and to inform clinical decision-making:

Biomedical knowledge graph integration: Chapter 3 constructs a heterogeneous, multi-modal knowledge graph using a Relational Graph Convolutional Network (R-GCN) to embed clinical and biological entities, including disease, drugs, genes, and single nucleotide polymorphisms (SNPs), into a unified representation that supports various link prediction tasks and downstream applications.