This study proposes an interpretable neural network-based non-proportional odds model (N$^3$POM) for ordinal regression. N$^3$POM is different from conventional approaches to ordinal regression with non-proportional models in several ways: (1) N$^3$POM is designed to directly handle continuous responses, whereas standard methods typically treat de facto ordered continuous variables as discrete, (2) instead of estimating response-dependent finite coefficients of linear models from discrete responses as is done in conventional approaches, we train a non-linear neural network to serve as a coefficient function. Thanks to the neural network, N$^3$POM offers flexibility while preserving the interpretability of conventional ordinal regression. We establish a sufficient condition under which the predicted conditional cumulative probability locally satisfies the monotonicity constraint over a user-specified region in the covariate space. Additionally, we provide a monotonicity-preserving stochastic (MPS) algorithm for effectively training the neural network. We apply N$^3$POM to several real-world datasets.

翻译：本研究提出了一种基于可解释神经网络的非比例优势模型（N$^3$POM），用于序数回归分析。N$^3$POM 与传统的非比例序数回归模型在多个方面存在差异：（1）N$^3$POM 可直接处理连续型响应变量，而标准方法通常将实际有序的连续变量视为离散变量；（2）传统方法基于离散响应估计线性模型中的响应相关有限系数，而本研究则训练非线性神经网络作为系数函数。借助神经网络，N$^3$POM 在保持传统序数回归可解释性的同时提供了灵活性。我们建立了充分条件，确保模型预测的条件累积概率在协变量空间中用户指定区域内局部满足单调性约束。此外，我们提出了一种保单调性随机（MPS）算法，用于有效训练该神经网络。最后，将 N$^3$POM 应用于多个真实世界数据集进行验证。