An interpretable neural network-based non-proportional odds model for ordinal regression
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913261318832128 |
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| author | Okuno, Akifumi Harada, Kazuharu |
| author_facet | Okuno, Akifumi Harada, Kazuharu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An interpretable neural network-based non-proportional odds model for ordinal regression Okuno, Akifumi Harada, Kazuharu Methodology Machine Learning 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. |
| title | An interpretable neural network-based non-proportional odds model for ordinal regression |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2303.17823 |