  This work extends causal inference with stochastic confounders. We propose a
new approach to variational estimation for causal inference based on a
representer theorem with a random input space. We estimate causal effects
involving latent confounders that may be interdependent and time-varying from
sequential, repeated measurements in an observational study. Our approach
extends current work that assumes independent, non-temporal latent confounders,
with potentially biased estimators. We introduce a simple yet elegant algorithm
without parametric specification on model components. Our method avoids the
need for expensive and careful parameterization in deploying complex models,
such as deep neural networks, for causal inference in existing approaches. We
demonstrate the effectiveness of our approach on various benchmark temporal
datasets.
