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Ordinal regression predicts the objects' labels that exhibit a naturalordering, which is important to many managerial problems such as credit scoringand clinical diagnosis. In these problems, the ability to explain how theattributes affect the prediction is critical to users. However, most, if notall, existing ordinal regression models simplify such explanation in the formof constant coefficients for the main and interaction effects of individualattributes. Such explanation cannot characterize the contributions ofattributes at different value scales. To address this challenge, we propose anew explainable ordinal regression model, namely, the Explainable OrdinalFactorization Model (XOFM). XOFM uses the piece-wise linear functions toapproximate the actual contributions of individual attributes and theirinteractions. Moreover, XOFM introduces a novel ordinal transformation processto assign each object the probabilities of belonging to multiple relevantclasses, instead of fixing boundaries to differentiate classes. XOFM is basedon the Factorization Machines to handle the potential sparsity problem as aresult of discretizing the attribute scales. Comprehensive experiments withbenchmark datasets and baseline models demonstrate that the proposed XOFMexhibits superior explainability and leads to state-of-the-art predictionaccuracy.

Explainable Ordinal Factorization Model: Deciphering the Effects of Attributes by Piece-wise Linear Approximation