Causal Domain Adaptation with Copula Entropy based Conditional Independence Test

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.