Laplace Variational Inference for Bayesian Envelope Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914361430245376 |
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| author | Kim, Seunghyeon Lee, Kwangmin Park, Yeonhee |
| author_facet | Kim, Seunghyeon Lee, Kwangmin Park, Yeonhee |
| contents | Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs sampling and Metropolis-Hastings algorithms suffer from slow mixing and high computational cost. Although automatic differentiation variational inference (ADVI) has been explored for Bayesian envelope models, the resulting gradient-based optimization is often numerically unstable due to severe ill-conditioning of the posterior distribution. To address this issue, we propose a novel reparameterization of the posterior distribution that alleviates the ill-conditioning inherent in conventional variational approaches. Building on this reparameterization, we develop an efficient variational inference procedure. Since the resulting likelihood remains nonconjugate, we approximate the corresponding variational factor using a Laplace approximation within a coordinate-ascent variational inference (CAVI) framework. We establish theoretical results showing that, at each one-step coordinate update, the Laplace approximation error relative to the exact variational inference coordinate update converges to zero. Simulation studies and a real-data analysis demonstrate that the proposed method substantially improves computational efficiency while maintaining estimation accuracy and model-selection performance relative to existing approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00927 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Laplace Variational Inference for Bayesian Envelope Models Kim, Seunghyeon Lee, Kwangmin Park, Yeonhee Methodology 62F15, 62H12, 62J05 Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs sampling and Metropolis-Hastings algorithms suffer from slow mixing and high computational cost. Although automatic differentiation variational inference (ADVI) has been explored for Bayesian envelope models, the resulting gradient-based optimization is often numerically unstable due to severe ill-conditioning of the posterior distribution. To address this issue, we propose a novel reparameterization of the posterior distribution that alleviates the ill-conditioning inherent in conventional variational approaches. Building on this reparameterization, we develop an efficient variational inference procedure. Since the resulting likelihood remains nonconjugate, we approximate the corresponding variational factor using a Laplace approximation within a coordinate-ascent variational inference (CAVI) framework. We establish theoretical results showing that, at each one-step coordinate update, the Laplace approximation error relative to the exact variational inference coordinate update converges to zero. Simulation studies and a real-data analysis demonstrate that the proposed method substantially improves computational efficiency while maintaining estimation accuracy and model-selection performance relative to existing approaches. |
| title | Laplace Variational Inference for Bayesian Envelope Models |
| topic | Methodology 62F15, 62H12, 62J05 |
| url | https://arxiv.org/abs/2603.00927 |