  Neural document ranking models perform impressively well due to superior
language understanding gained from pre-training tasks. However, due to their
complexity and large number of parameters, these (typically transformer-based)
models are often non-interpretable in that ranking decisions can not be clearly
attributed to specific parts of the input documents.
  In this paper we propose ranking models that are inherently interpretable by
generating explanations as a by-product of the prediction decision. We
introduce the Select-and-Rank paradigm for document ranking, where we first
output an explanation as a selected subset of sentences in a document.
Thereafter, we solely use the explanation or selection to make the prediction,
making explanations first-class citizens in the ranking process. Technically,
we treat sentence selection as a latent variable trained jointly with the
ranker from the final output. To that end, we propose an end-to-end training
technique for Select-and-Rank models utilizing reparameterizable subset
sampling using the Gumbel-max trick.
  We conduct extensive experiments to demonstrate that our approach is
competitive to state-of-the-art methods. Our approach is broadly applicable to
numerous ranking tasks and furthers the goal of building models that are
interpretable by design. Finally, we present real-world applications that
benefit from our sentence selection method.
