Hamiltonian Monte Carlo Inference of Marginalized Linear Mixed-Effects Models
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912286613962752 |
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| author | Lai, Jinlin Domke, Justin Sheldon, Daniel |
| author_facet | Lai, Jinlin Domke, Justin Sheldon, Daniel |
| contents | Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language and then sample via Hamiltonian Monte Carlo (HMC). However, there are many ways a user can transform a model that make inference more or less efficient. In particular, marginalizing some variables can greatly improve inference but is difficult for users to do manually. We develop an algorithm to easily marginalize random effects in LMMs. A naive approach introduces cubic time operations within an inference algorithm like HMC, but we reduce the running time to linear using fast linear algebra techniques. We show that marginalization is always beneficial when applicable and highlight improvements in various models, especially ones from cognitive sciences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Monte Carlo Inference of Marginalized Linear Mixed-Effects Models Lai, Jinlin Domke, Justin Sheldon, Daniel Machine Learning Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language and then sample via Hamiltonian Monte Carlo (HMC). However, there are many ways a user can transform a model that make inference more or less efficient. In particular, marginalizing some variables can greatly improve inference but is difficult for users to do manually. We develop an algorithm to easily marginalize random effects in LMMs. A naive approach introduces cubic time operations within an inference algorithm like HMC, but we reduce the running time to linear using fast linear algebra techniques. We show that marginalization is always beneficial when applicable and highlight improvements in various models, especially ones from cognitive sciences. |
| title | Hamiltonian Monte Carlo Inference of Marginalized Linear Mixed-Effects Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.24079 |