  We derive a family of loss functions to train models in the presence of
sampling bias. Examples are when the prevalence of a pathology differs from its
sampling rate in the training dataset, or when a machine learning practioner
rebalances their training dataset. Sampling bias causes large discrepancies
between model performance in the lab and in more realistic settings. It is
omnipresent in medical imaging applications, yet is often overlooked at
training time or addressed on an ad-hoc basis. Our approach is based on
Bayesian risk minimization. For arbitrary likelihood models we derive the
associated bias corrected loss for training, exhibiting a direct connection to
information gain. The approach integrates seamlessly in the current paradigm of
(deep) learning using stochastic backpropagation and naturally with Bayesian
models. We illustrate the methodology on case studies of lung nodule malignancy
grading.
