  Domain Adaptation (DA) is a typical problem in machine learning that aims to
transfer the model trained on source domain to target domain with different
distribution. Causal DA is a special case of DA that solves the problem from
the view of causality. It embeds the probabilistic relationships in multiple
domains in a larger causal structure network of a system and tries to find the
causal source (or intervention) on the system as the reason of distribution
drifts of the system states across domains. In this sense, causal DA is
transformed as a causal discovery problem that finds invariant representation
across domains through the conditional independence between the state variables
and observable state of the system given interventions. Testing conditional
independence is the corner stone of causal discovery. Recently, a copula
entropy based conditional independence test was proposed with a rigorous theory
and a non-parametric estimation method. In this paper, we first present a
mathemetical model for causal DA problem and then propose a method for causal
DA that finds the invariant representation across domains with the copula
entropy based conditional independence test. The effectiveness of the method is
verified on two simulated data. The power of the proposed method is then
demonstrated on two real-world data: adult census income data and gait
characteristics data.
