Causal Expectation-Maximisation
  Structural causal models are the fundamental modelling unit in Pearl's causal
theory; in principle they allow us to solve any causal inference query, such as
causal effects or counterfactuals. But they most often contain latent variables
that limit their application to special settings. In this paper we introduce
the causal EM algorithm that aims at reconstructing the uncertainty about the
latent variables; based on this, causal inference can approximately be solved
via standard algorithms for Bayesian networks. The result is, for the first
time, a completely general method to solve causal inference queries, be they
identifiable or not (in which case we deliver bounds), on semi-Markovian
structural causal models with categorical variables. We show empirically that
the approximation we provide becomes accurate in a fair number of EM runs. We
discuss the application of the causal EM to a real medical problem. Finally, we
show that causal inference is NP-hard also in models characterised by
polytree-shaped graphs; this supports developing approximate approaches to
causal inference.
