Affine calculus for constrained minima of the Kullback-Leibler divergence
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912308819656704 |
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| author | Pistone, Giovanni |
| author_facet | Pistone, Giovanni |
| contents | The non-parametric version of Amari's dually affine Information Geometry provides a practical calculus to perform computations of interest in statistical machine learning. The method uses the notion of a statistical bundle, a mathematical structure that includes both probability densities and random variables to capture the spirit of Fisherian statistics. We focus on computations involving a constrained minimization of the Kullback-Leibler divergence. We show how to obtain neat and principled versions of known computation in applications such as mean-field approximation, adversarial generative models, and variational Bayes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affine calculus for constrained minima of the Kullback-Leibler divergence Pistone, Giovanni Statistics Theory The non-parametric version of Amari's dually affine Information Geometry provides a practical calculus to perform computations of interest in statistical machine learning. The method uses the notion of a statistical bundle, a mathematical structure that includes both probability densities and random variables to capture the spirit of Fisherian statistics. We focus on computations involving a constrained minimization of the Kullback-Leibler divergence. We show how to obtain neat and principled versions of known computation in applications such as mean-field approximation, adversarial generative models, and variational Bayes. |
| title | Affine calculus for constrained minima of the Kullback-Leibler divergence |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2502.02177 |