2-Cats: 2D Copula Approximating Transforms
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913366110371840 |
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| author | Figueiredo, Flavio Fernandes, José Geraldo Silva, Jackson Assunção, Renato M. |
| author_facet | Figueiredo, Flavio Fernandes, José Geraldo Silva, Jackson Assunção, Renato M. |
| contents | Copulas are powerful statistical tools for capturing dependencies across data dimensions. Applying Copulas involves estimating independent marginals, a straightforward task, followed by the much more challenging task of determining a single copulating function, $C$, that links these marginals. For bivariate data, a copula takes the form of a two-increasing function $C: (u,v)\in \mathbb{I}^2 \rightarrow \mathbb{I}$, where $\mathbb{I} = [0, 1]$. This paper proposes 2-Cats, a Neural Network (NN) model that learns two-dimensional Copulas without relying on specific Copula families (e.g., Archimedean). Furthermore, via both theoretical properties of the model and a Lagrangian training approach, we show that 2-Cats meets the desiderata of Copula properties. Moreover, inspired by the literature on Physics-Informed Neural Networks and Sobolev Training, we further extend our training strategy to learn not only the output of a Copula but also its derivatives. Our proposed method exhibits superior performance compared to the state-of-the-art across various datasets while respecting (provably for most and approximately for a single other) properties of C. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16391 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 2-Cats: 2D Copula Approximating Transforms Figueiredo, Flavio Fernandes, José Geraldo Silva, Jackson Assunção, Renato M. Machine Learning Artificial Intelligence Copulas are powerful statistical tools for capturing dependencies across data dimensions. Applying Copulas involves estimating independent marginals, a straightforward task, followed by the much more challenging task of determining a single copulating function, $C$, that links these marginals. For bivariate data, a copula takes the form of a two-increasing function $C: (u,v)\in \mathbb{I}^2 \rightarrow \mathbb{I}$, where $\mathbb{I} = [0, 1]$. This paper proposes 2-Cats, a Neural Network (NN) model that learns two-dimensional Copulas without relying on specific Copula families (e.g., Archimedean). Furthermore, via both theoretical properties of the model and a Lagrangian training approach, we show that 2-Cats meets the desiderata of Copula properties. Moreover, inspired by the literature on Physics-Informed Neural Networks and Sobolev Training, we further extend our training strategy to learn not only the output of a Copula but also its derivatives. Our proposed method exhibits superior performance compared to the state-of-the-art across various datasets while respecting (provably for most and approximately for a single other) properties of C. |
| title | 2-Cats: 2D Copula Approximating Transforms |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2309.16391 |