  We study causal inference in a multi-environment setting, in which the
functional relations for producing the variables from their direct causes
remain the same across environments, while the distribution of exogenous noises
may vary. We introduce the idea of using the invariance of the functional
relations of the variables to their causes across a set of environments. We
define a notion of completeness for a causal inference algorithm in this
setting and prove the existence of such algorithm by proposing the baseline
algorithm. Additionally, we present an alternate algorithm that has
significantly improved computational and sample complexity compared to the
baseline algorithm. The experiment results show that the proposed algorithm
outperforms the other existing algorithms.
