Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learning
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910581747875840 |
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| author | Matsubara, Takuo |
| author_facet | Matsubara, Takuo |
| contents | Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to alternative pseudo residuals that are Wasserstein gradients of loss functionals of probability distributions assigned at each input. It solves distribution-valued supervised learning, where the output values of the training dataset are probability distributions for each input. In classification and regression, a model typically returns, for each input, a point estimate of a parameter of a noise distribution specified for a response variable, such as the class probability parameter of a categorical distribution specified for a response label. A main application of Wasserstein gradient boosting in this paper is tree-based evidential learning, which returns a distributional estimate of the response parameter for each input. We empirically demonstrate the superior performance of the probabilistic prediction by Wasserstein gradient boosting in comparison with existing uncertainty quantification methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_09536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learning Matsubara, Takuo Methodology Machine Learning Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to alternative pseudo residuals that are Wasserstein gradients of loss functionals of probability distributions assigned at each input. It solves distribution-valued supervised learning, where the output values of the training dataset are probability distributions for each input. In classification and regression, a model typically returns, for each input, a point estimate of a parameter of a noise distribution specified for a response variable, such as the class probability parameter of a categorical distribution specified for a response label. A main application of Wasserstein gradient boosting in this paper is tree-based evidential learning, which returns a distributional estimate of the response parameter for each input. We empirically demonstrate the superior performance of the probabilistic prediction by Wasserstein gradient boosting in comparison with existing uncertainty quantification methods. |
| title | Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learning |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2405.09536 |