  Estimating the Individual Treatment Effect from observational data, defined
as the difference between outcomes with and without treatment or intervention,
while observing just one of both, is a challenging problems in causal learning.
In this paper, we formulate this problem as an inference from hidden variables
and enforce causal constraints based on a model of four exclusive causal
populations. We propose a new version of the EM algorithm, coined as
Expected-Causality-Maximization (ECM) algorithm and provide hints on its
convergence under mild conditions. We compare our algorithm to baseline methods
on synthetic and real-world data and discuss its performances.
