  Entropic causal inference is a framework for inferring the causal direction
between two categorical variables from observational data. The central
assumption is that the amount of unobserved randomness in the system is not too
large. This unobserved randomness is measured by the entropy of the exogenous
variable in the underlying structural causal model, which governs the causal
relation between the observed variables. Kocaoglu et al. conjectured that the
causal direction is identifiable when the entropy of the exogenous variable is
not too large. In this paper, we prove a variant of their conjecture. Namely,
we show that for almost all causal models where the exogenous variable has
entropy that does not scale with the number of states of the observed
variables, the causal direction is identifiable from observational data. We
also consider the minimum entropy coupling-based algorithmic approach presented
by Kocaoglu et al., and for the first time demonstrate algorithmic
identifiability guarantees using a finite number of samples. We conduct
extensive experiments to evaluate the robustness of the method to relaxing some
of the assumptions in our theory and demonstrate that both the constant-entropy
exogenous variable and the no latent confounder assumptions can be relaxed in
practice. We also empirically characterize the number of observational samples
needed for causal identification. Finally, we apply the algorithm on Tuebingen
cause-effect pairs dataset.
