  Statistical prediction models are often trained on data from different
probability distributions than their eventual use cases. One approach to
proactively prepare for these shifts harnesses the intuition that causal
mechanisms should remain invariant between environments. Here we focus on a
challenging setting in which the causal and anticausal variables of the target
are unobserved. Leaning on information theory, we develop feature selection and
engineering techniques for the observed downstream variables that act as
proxies. We identify proxies that help to build stable models and moreover
utilize auxiliary training tasks to answer counterfactual questions that
extract stability-enhancing information from proxies. We demonstrate the
effectiveness of our techniques on synthetic and real data.
