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 defined for both continuous and discrete responses, whereas standard methods typically treat the ordered continuous variables as if they are discrete, (2) instead of estimating response-dependent finite-dimensional 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（N³POM）用于序数回归。N³POM与传统的非比例序数回归方法在以下几个方面存在显著差异：（1）N³POM同时适用于连续型与离散型响应变量，而标准方法通常将有序连续变量视为离散变量处理；（2）与传统的从离散响应中估计响应依赖的有限维线性模型系数不同，我们训练了一个非线性神经网络作为系数函数。借助神经网络，N³POM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，确保在协变量空间用户指定区域内，预测的条件累积概率局部满足单调性约束。此外，我们提出了一种保持单调性的随机算法（MPS）用于有效训练神经网络。我们将N³POM应用于多个真实数据集。