  Ordinal regression predicts the objects' labels that exhibit a natural
ordering, which is important to many managerial problems such as credit scoring
and clinical diagnosis. In these problems, the ability to explain how the
attributes affect the prediction is critical to users. However, most, if not
all, existing ordinal regression models simplify such explanation in the form
of constant coefficients for the main and interaction effects of individual
attributes. Such explanation cannot characterize the contributions of
attributes at different value scales. To address this challenge, we propose a
new explainable ordinal regression model, namely, the Explainable Ordinal
Factorization Model (XOFM). XOFM uses the piece-wise linear functions to
approximate the actual contributions of individual attributes and their
interactions. Moreover, XOFM introduces a novel ordinal transformation process
to assign each object the probabilities of belonging to multiple relevant
classes, instead of fixing boundaries to differentiate classes. XOFM is based
on the Factorization Machines to handle the potential sparsity problem as a
result of discretizing the attribute scales. Comprehensive experiments with
benchmark datasets and baseline models demonstrate that the proposed XOFM
exhibits superior explainability and leads to state-of-the-art prediction
accuracy.
