A0508
Title: Directed acyclic graphs with unmeasured confounders using instrumental variables
Authors: Kean Ming Tan - University of Michigan (United States) [presenting]
Abstract: Directly acyclic graphs play an important role to describe causal relationships among a set of random variables. Existing work has mainly focused on estimating directed acyclic graphs under the assumption that all of the relevant variables are observed. However, in many scientific settings, there may be unobserved variables that are associated with the observed variables. Without adjusting the unobserved variables, the estimated causal relationships among the set of observed variables may be spurious. To address the aforementioned issue, we propose to estimate a directly acyclic graph under the presence of unmeasured confounders using an instrumental variable approach. The approach is motivated by an application in neuroscience: using optogenetics, neuroscientists can design and activate specific neurons with optical stimulation, which can be treated as instrumental variables. Specifically, we show that the ancestral relationships can be recovered with a computationally efficient screening procedure. The screening procedure is then combined with the generalized two-stage least squares method to ensure computationally efficient recovery of the model parameters subjected to the acyclic constraint of a directed acyclic graph. We illustrate the performance of the proposed method via extensive numerical studies and an application to the aforementioned neuroscience data.
