An interpretable neural network-based non-proportional odds model for ordinal regression

• DOI: 10.48550/arxiv.2303.17823
• Publication Date: 2024-03-29
• Authors: Akifumi Okuno; Kazuharu Harada
• Keywords: Methodology (stat.ME); FOS: Computer and information sciences; Computer Science - Machine Learning; Statistics - Machine Learning; Machine Learning (stat.ML); Statistics - Methodology; Machine Learning (cs.LG)

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.<br/>35 pages, 18 figures, accepted to Journal of Computational and Graphical Statistics<br/>