Structural Causal Models Are (Solvable by) Credal Networks
  A structural causal model is made of endogenous (manifest) and exogenous
(latent) variables. We show that endogenous observations induce linear
constraints on the probabilities of the exogenous variables. This allows to
exactly map a causal model into a credal network. Causal inferences, such as
interventions and counterfactuals, can consequently be obtained by standard
algorithms for the updating of credal nets. These natively return sharp values
in the identifiable case, while intervals corresponding to the exact bounds are
produced for unidentifiable queries. A characterization of the causal models
that allow the map above to be compactly derived is given, along with a
discussion about the scalability for general models. This contribution should
be regarded as a systematic approach to represent structural causal models by
credal networks and hence to systematically compute causal inferences. A number
of demonstrative examples is presented to clarify our methodology. Extensive
experiments show that approximate algorithms for credal networks can
immediately be used to do causal inference in real-size problems.
