  One of the most important problems in transfer learning is the task of domain
adaptation, where the goal is to apply an algorithm trained in one or more
source domains to a different (but related) target domain. This paper deals
with domain adaptation in the presence of covariate shift while there exist
invariances across domains. A main limitation of existing causal inference
methods for solving this problem is scalability. To overcome this difficulty,
we propose SCTL, an algorithm that avoids an exhaustive search and identifies
invariant causal features across the source and target domains based on Markov
blanket discovery. SCTL does not require to have prior knowledge of the causal
structure, the type of interventions, or the intervention targets. There is an
intrinsic locality associated with SCTL that makes SCTL practically scalable
and robust because local causal discovery increases the power of computational
independence tests and makes the task of domain adaptation computationally
tractable. We show the scalability and robustness of SCTL for domain adaptation
using synthetic and real data sets in low-dimensional and high-dimensional
settings.
