Causal Mediation Analysis with Multi-dimensional and Indirectly Observed
  Mediators
Ziyang Jiang Yiling Liu Michael H. Klein Ahmed Aloui Yiman Ren Keyu Li Vahid Tarokh David Carlson
Causal mediation analysis (CMA) is a powerful method to dissect the total
effect of a treatment into direct and mediated effects within the potential
outcome framework. This is important in many scientific applications to
identify the underlying mechanisms of a treatment effect. However, in many
scientific applications the mediator is unobserved, but there may exist related
measurements. For example, we may want to identify how changes in brain
activity or structure mediate an antidepressant's effect on behavior, but we
may only have access to electrophysiological or imaging brain measurements. To
date, most CMA methods assume that the mediator is one-dimensional and
observable, which oversimplifies such real-world scenarios. To overcome this
limitation, we introduce a CMA framework that can handle complex and indirectly
observed mediators based on the identifiable variational autoencoder (iVAE)
architecture. We prove that the true joint distribution over observed and
latent variables is identifiable with the proposed method. Additionally, our
framework captures a disentangled representation of the indirectly observed
mediator and yields accurate estimation of the direct and mediated effects in
synthetic and semi-synthetic experiments, providing evidence of its potential
utility in real-world applications.