Bernstein Flows for Flexible Posteriors in Variational Bayes
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910341054595072 |
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| author | Dürr, Oliver Hörling, Stephan Dold, Daniel Kovylov, Ivonne Sick, Beate |
| author_facet | Dürr, Oliver Hörling, Stephan Dold, Daniel Kovylov, Ivonne Sick, Beate |
| contents | Variational inference (VI) is a technique to approximate difficult to compute posteriors by optimization. In contrast to MCMC, VI scales to many observations. In the case of complex posteriors, however, state-of-the-art VI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method, flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art VI methods including normalizing flow based VI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI outperforms other VI methods. Further, we develop with BF-VI a Bayesian model for the semi-structured Melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate for the first time how the use of VI in semi-structured models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05650 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bernstein Flows for Flexible Posteriors in Variational Bayes Dürr, Oliver Hörling, Stephan Dold, Daniel Kovylov, Ivonne Sick, Beate Machine Learning Variational inference (VI) is a technique to approximate difficult to compute posteriors by optimization. In contrast to MCMC, VI scales to many observations. In the case of complex posteriors, however, state-of-the-art VI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method, flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art VI methods including normalizing flow based VI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI outperforms other VI methods. Further, we develop with BF-VI a Bayesian model for the semi-structured Melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate for the first time how the use of VI in semi-structured models. |
| title | Bernstein Flows for Flexible Posteriors in Variational Bayes |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2202.05650 |