  Despite the pervasiveness of ordinal labels in supervised learning, it
remains common practice in deep learning to treat such problems as categorical
classification using the categorical cross entropy loss. Recent methods
attempting to address this issue while respecting the ordinal structure of the
labels have resorted to converting ordinal regression into a series of extended
binary classification subtasks. However, the adoption of such methods remains
inconsistent due to theoretical and practical limitations. Here we address
these limitations by demonstrating that the subtask probabilities form a Markov
chain. We show how to straightforwardly modify neural network architectures to
exploit this fact and thereby constrain predictions to be universally rank
consistent. We furthermore prove that all rank consistent solutions can be
represented within this formulation, and derive a loss function producing
maximum likelihood parameter estimates. Using diverse benchmarks and the
real-world application of a specialized recurrent neural network for COVID-19
prognosis, we demonstrate the practical superiority of this method versus the
current state-of-the-art. The method is open sourced as user-friendly PyTorch
and TensorFlow packages.
