From Statistical Transportability to
Estimating the Effect of Stochastic Interventions
Abstract
Learning systems often face a critical challenge
when applied to settings that differ from those under which they were initially trained. In particular, the assumption that both the source/training
and the target/deployment domains follow the same
causal mechanisms and observed distributions is
commonly violated. This implies that the robustness and convergence guarantees usually expected
from these methods are no longer attainable. In
this paper, we study these violations through causal
lens using the formalism of statistical transportability [Pearl and Bareinboim, 2011] (PB, for short).
We start by proving sufficient and necessary graphical conditions under which a probability distribution observed in the source domain can be extrapolated to the target one, where strictly less data is
available. We develop the first sound and complete
procedure for statistical transportability, which formally closes the problem introduced by PB. Further, we tackle the general challenge of identification of stochastic interventions from observational
data [Sec. 4.4, Pearl, 2000]. This problem has been
solved in the context of atomic interventions using Pearl’s do-calculus, which lacks complete treatment in the stochastic case. We prove completeness
of stochastic identification by constructing a reduction of any instance of this problem to an instance
of statistical transportability, closing the problem