  Healthcare data often come from multiple sites in which the correlations
between confounding variables can vary widely. If deep learning models exploit
these unstable correlations, they might fail catastrophically in unseen sites.
Although many methods have been proposed to tackle unstable correlations, each
has its limitations. For example, adversarial training forces models to
completely ignore unstable correlations, but doing so may lead to poor
predictive performance. Other methods (e.g. Invariant risk minimization [4])
try to learn domain-invariant representations that rely only on stable
associations by assuming a causal data-generating process (input X causes class
label Y ). Thus, they may be ineffective for anti-causal tasks (Y causes X),
which are common in computer vision. We propose a method called CoPA
(Conditional Prevalence-Adjustment) for anti-causal tasks. CoPA assumes that
(1) generation mechanism is stable, i.e. label Y and confounding variable(s) Z
generate X, and (2) the unstable conditional prevalence in each site E fully
accounts for the unstable correlations between X and Y . Our crucial
observation is that confounding variables are routinely recorded in healthcare
settings and the prevalence can be readily estimated, for example, from a set
of (Y, Z) samples (no need for corresponding samples of X). CoPA can work even
if there is a single training site, a scenario which is often overlooked by
existing methods. Our experiments on synthetic and real data show CoPA beating
competitive baselines.
