Causal Discovery with Diverse Types of Outcomes and Unmeasured Confounders

Music City Center 

Causal discovery, the process of identifying causal relationships among variables, is a fundamental problem in statistics. Yet, statistical challenges remain when the data is of mixed data types and affected by unmeasured confounders. In this talk, we address these issues by presenting a novel causal discovery method via instrumental variables with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data, in the presence of confounders. In particular, we introduce two peeling algorithms (bottom-up and top-down) to ascertain causal relationships and valid instruments. Our approach first reconstructs a super-graph to represent ancestral relationships between variables, using a peeling algorithm based on nodewise constrained GLM regressions that exploit relationships between primary and instrumental variables. Then, it estimates parent-child effects from the ancestral relationships using another peeling algorithm that deconfounds a child's model with information borrowed from its parents' models. We also present a theoretical analysis of the proposed approach, establishing conditions for model identifiability and providing statistical guarantees for accurately discovering parent-child relationships via the peeling algorithms. Finally, we demonstrate an application to Alzheimer's disease genomics data, highlighting the method's utility in constructing gene-to-gene and gene-to-disease regulatory networks.

Directed acyclic graphs

generalized linear models

mixed graphical models

hierarchy

nonconvex minimization