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

TL;DR

This paper introduces N³POM, an interpretable neural network model for ordinal regression that handles both continuous and discrete responses, offering flexibility and interpretability with a novel training algorithm.

Contribution

The paper presents a new neural network-based non-proportional odds model that extends ordinal regression to continuous responses while maintaining interpretability.

Findings

N³POM effectively models both continuous and discrete responses.

The model preserves interpretability through neural network coefficient functions.

A monotonicity-preserving training algorithm improves model performance.

Abstract

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.