Robust Causal Domain Adaptation in a Simple Diagnostic Setting.

Causal domain adaptation approaches aim to find statistical relations in a source domain, that will still hold in a target domain, using the assumption that a common causal graph underlies both domains. For many such problems, the available information is insufficient to uniquely identify the target domain distribution, and we find a set of distributions instead. We propose to use a worst-case approach, picking an action that performs well against all distributions in this set. In this paper, we study a specific diagnostic instance of this problem, and find a sufficient and necessary condition that characterizes the worst-case distribution in the target domain. We find that the Brier and logarithmic scores lead to different distributions, and consequently to different recommendations for the decision maker.