antGLasso: An Efficient Tensor Graphical Lasso Algorithm

The class of bigraphical lasso algorithms (and, more broadly, 'tensor'-graphical lasso algorithms) has been used to estimate dependency structures within matrix and tensor data. However, all current methods to do so take prohibitively long on modestly sized datasets. We present a novel tensor-graphical lasso algorithm that analytically estimates the dependency structure, unlike its iterative predecessors. This provides a speedup of multiple orders of magnitude, allowing this class of algorithms to be used on large, real-world datasets.Comment: 9 pages (21 including supplementary material), 8 figures, submitted to the GLFrontiers workshop at NeurIPS 202

Causal Inference under Data Restrictions

This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we propose a method under the principal stratification framework to identify and estimate the average treatment effects on a binary outcome, conditional on the counterfactual status of a post-treatment intermediate response. Under mild assumptions, the treatment effect of interest can be identified. We extend the approach to address censored outcome data. The proposed method is applied to a neoadjuvant clinical trial and its performance is evaluated via simulation studies. In the second project, we propose a tree-based model averaging approach to improve the estimation accuracy of conditional average treatment effects at a target site by leveraging models derived from other potentially heterogeneous sites, without them sharing subject-level data. The performance of this approach is demonstrated by a study of the causal effects of oxygen therapy on hospital survival rates and backed up by comprehensive simulations. In the third project, we propose a robust individualized decision learning framework with sensitive variables to improve the worst-case outcomes of individuals caused by sensitive variables that are unavailable at the time of decision. Unlike most existing work that uses mean-optimal objectives, we propose a robust learning framework by finding a newly defined quantile- or infimum-optimal decision rule. From a causal perspective, we also generalize the classic notion of (average) fairness to conditional fairness for individual subjects. The reliable performance of the proposed method is demonstrated through synthetic experiments and three real-data applications.Comment: PhD dissertation, University of Pittsburgh. The contents are mostly based on arXiv:2211.06569, arXiv:2103.06261 and arXiv:2103.04175 with extended discussion