Bayesian Multinomial Logistic Regression for Numerous Categories
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866918357594275840 |
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| author | Fisher, Jared D. McEvoy, Kyle R. |
| author_facet | Fisher, Jared D. McEvoy, Kyle R. |
| contents | Bayesian multinomial logistic regression provides a principled, interpretable approach to multiclass classification, but posterior sampling becomes increasingly expensive as the model dimension grows. Prior work has studied scalability in the number of subjects and covariates; in contrast, this paper focuses on how computation changes as the number of outcome categories increases. To improve scalability in settings with numerous categories, we adapt a gamma-augmentation strategy to decouple category-specific coefficient updates, so that each category's coefficients can be updated conditional on a single auxiliary variable per subject, rather than on the full set of other categories' coefficients. Because the resulting coefficient conditionals are non-conjugate, we couple this augmentation with either adaptive Metropolis-Hastings or elliptical slice sampling. Through simulation and a real-data example, we compare effective sample size and effective sampling rate across several standard competitors. We find that the best-performing sampler depends on the dimension and imbalance regime, and that the proposed augmentation provides substantial speedups in scenarios with numerous categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14537 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bayesian Multinomial Logistic Regression for Numerous Categories Fisher, Jared D. McEvoy, Kyle R. Computation Methodology Bayesian multinomial logistic regression provides a principled, interpretable approach to multiclass classification, but posterior sampling becomes increasingly expensive as the model dimension grows. Prior work has studied scalability in the number of subjects and covariates; in contrast, this paper focuses on how computation changes as the number of outcome categories increases. To improve scalability in settings with numerous categories, we adapt a gamma-augmentation strategy to decouple category-specific coefficient updates, so that each category's coefficients can be updated conditional on a single auxiliary variable per subject, rather than on the full set of other categories' coefficients. Because the resulting coefficient conditionals are non-conjugate, we couple this augmentation with either adaptive Metropolis-Hastings or elliptical slice sampling. Through simulation and a real-data example, we compare effective sample size and effective sampling rate across several standard competitors. We find that the best-performing sampler depends on the dimension and imbalance regime, and that the proposed augmentation provides substantial speedups in scenarios with numerous categories. |
| title | Bayesian Multinomial Logistic Regression for Numerous Categories |
| topic | Computation Methodology |
| url | https://arxiv.org/abs/2208.14537 |