This paper proposes an interpretable neural network-based non-proportional odds model (N$^3$POM) for ordinal regression, where the response variable can take not only discrete but also continuous values, and the regression coefficients vary depending on the predicting ordinal response. In contrast to conventional approaches estimating the linear coefficients of regression directly from the discrete response, we train a non-linear neural network that outputs the linear coefficients by taking the response as its input. By virtue of the neural network, N$^3$POM may have flexibility while preserving the interpretability of the conventional ordinal regression. We show a sufficient condition so that the predicted conditional cumulative probability~(CCP) satisfies the monotonicity constraint locally over a user-specified region in the covariate space; we also provide a monotonicity-preserving stochastic (MPS) algorithm for training the neural network adequately.

翻译：本文提出了一种基于可解释神经网络的非比例优势序数回归模型（N$^3$POM），该模型适用于响应变量既可为离散值也可为连续值的序数回归场景，且回归系数随预测序数响应的变化而变化。传统方法直接从离散响应中估计回归的线性系数，而本文方法则训练一个非线性神经网络，以响应为输入并输出线性系数。借助神经网络结构，N$^3$POM在保持传统序数回归可解释性的同时提升了灵活性。我们给出了一个充分条件，使得预测的条件累积概率（CCP）在协变量空间中用户指定的局部区域内满足单调性约束；同时提出了一种保持单调性的随机（MPS）算法，用于充分训练该神经网络。