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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.00660 |
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| _version_ | 1866910627075719168 |
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| author | Wasserman, Max Mateos, Gonzalo |
| author_facet | Wasserman, Max Mateos, Gonzalo |
| contents | Large-scale latent variable models require expressive continuous distributions that support efficient sampling and low-variance differentiation, achievable through the reparameterization trick. The Kumaraswamy (KS) distribution is both expressive and supports the reparameterization trick with a simple closed-form inverse CDF. Yet, its adoption remains limited. We identify and resolve numerical instabilities in the inverse CDF and log-pdf, exposing issues in libraries like PyTorch and TensorFlow. We then introduce simple and scalable latent variable models based on the KS, improving exploration-exploitation trade-offs in contextual multi-armed bandits and enhancing uncertainty quantification for link prediction with graph neural networks. Our results support the stabilized KS distribution as a core component in scalable variational models for bounded latent variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilizing the Kumaraswamy Distribution Wasserman, Max Mateos, Gonzalo Machine Learning Large-scale latent variable models require expressive continuous distributions that support efficient sampling and low-variance differentiation, achievable through the reparameterization trick. The Kumaraswamy (KS) distribution is both expressive and supports the reparameterization trick with a simple closed-form inverse CDF. Yet, its adoption remains limited. We identify and resolve numerical instabilities in the inverse CDF and log-pdf, exposing issues in libraries like PyTorch and TensorFlow. We then introduce simple and scalable latent variable models based on the KS, improving exploration-exploitation trade-offs in contextual multi-armed bandits and enhancing uncertainty quantification for link prediction with graph neural networks. Our results support the stabilized KS distribution as a core component in scalable variational models for bounded latent variables. |
| title | Stabilizing the Kumaraswamy Distribution |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.00660 |