  As statistical classifiers become integrated into real-world applications, it
is important to consider not only their accuracy but also their robustness to
changes in the data distribution. In this paper, we consider the case where
there is an unobserved confounding variable $z$ that influences both the
features $\mathbf{x}$ and the class variable $y$. When the influence of $z$
changes from training to testing data, we find that the classifier accuracy can
degrade rapidly. In our approach, we assume that we can predict the value of
$z$ at training time with some error. The prediction for $z$ is then fed to
Pearl's back-door adjustment to build our model. Because of the attenuation
bias caused by measurement error in $z$, standard approaches to controlling for
$z$ are ineffective. In response, we propose a method to properly control for
the influence of $z$ by first estimating its relationship with the class
variable $y$, then updating predictions for $z$ to match that estimated
relationship. By adjusting the influence of $z$, we show that we can build a
model that exceeds competing baselines on accuracy as well as on robustness
over a range of confounding relationships.
