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Domain Adaptation (DA) is a typical problem in machine learning that aims totransfer the model trained on source domain to target domain with differentdistribution. Causal DA is a special case of DA that solves the problem fromthe view of causality. It embeds the probabilistic relationships in multipledomains in a larger causal structure network of a system and tries to find thecausal source (or intervention) on the system as the reason of distributiondrifts of the system states across domains. In this sense, causal DA istransformed as a causal discovery problem that finds invariant representationacross domains through the conditional independence between the state variablesand observable state of the system given interventions. Testing conditionalindependence is the corner stone of causal discovery. Recently, a copulaentropy based conditional independence test was proposed with a rigorous theoryand a non-parametric estimation method. In this paper, we first present amathemetical model for causal DA problem and then propose a method for causalDA that finds the invariant representation across domains with the copulaentropy based conditional independence test. The effectiveness of the method isverified on two simulated data. The power of the proposed method is thendemonstrated on two real-world data: adult census income data and gaitcharacteristics data.

Causal Domain Adaptation with Copula Entropy based Conditional Independence Test