Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914555981987840 |
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| author | Porwal, Anupreet Rodriguez, Abel |
| author_facet | Porwal, Anupreet Rodriguez, Abel |
| contents | This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various (data-selected) blocks of parameters while fully accounting for the predictors' correlation structure, providing a bridge between the literatures on model selection and continuous shrinkage priors. We show that Dirichlet process mixtures of block $g$ priors are consistent in various senses and, in particular, that they avoid the conditional Lindley ``paradox'' highlighted by Som et al. (2016). Further, we develop a Markov chain Monte Carlo algorithm for posterior inference that requires only minimal ad-hoc tuning. Finally, we investigate the empirical performance of the prior in various real and simulated datasets. In the presence of a small number of very large effects, Dirichlet process mixtures of block $g$ priors lead to higher power for detecting smaller but significant effects without only a minimal increase in the number of false discoveries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models Porwal, Anupreet Rodriguez, Abel Methodology Machine Learning This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various (data-selected) blocks of parameters while fully accounting for the predictors' correlation structure, providing a bridge between the literatures on model selection and continuous shrinkage priors. We show that Dirichlet process mixtures of block $g$ priors are consistent in various senses and, in particular, that they avoid the conditional Lindley ``paradox'' highlighted by Som et al. (2016). Further, we develop a Markov chain Monte Carlo algorithm for posterior inference that requires only minimal ad-hoc tuning. Finally, we investigate the empirical performance of the prior in various real and simulated datasets. In the presence of a small number of very large effects, Dirichlet process mixtures of block $g$ priors lead to higher power for detecting smaller but significant effects without only a minimal increase in the number of false discoveries. |
| title | Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2411.00471 |