Fréchet regression with implicit denoising and multicollinearity reduction
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866909556702969856 |
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| author | Mansouri, Dou El Kefel Benkabou, Seif-Eddine Benabdeslem, Khalid |
| author_facet | Mansouri, Dou El Kefel Benkabou, Seif-Eddine Benabdeslem, Khalid |
| contents | Fréchet regression extends linear regression to model complex responses
in metric spaces, making it particularly relevant for multi-label regression,
where eachinstance can have multiple associated labels. However, addressing
noise and dependencies among predictors within this framework remains un derexplored. In this paper, we present an extension of the Global Fréchet re gression model that enables explicit modeling of relationships between input
variables and multiple responses. To address challenges arising from noise
and multicollinearity, we propose a novel framework based on implicit regu larization, which preserves the intrinsic structure of the data while effectively
capturing complex dependencies. Our approach ensures accurate and efficient
modeling without the biases introduced by traditional explicit regularization
methods. Theoretical guarantees are provided, and the performance of the
proposed method is demonstrated through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18247 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fréchet regression with implicit denoising and multicollinearity reduction Mansouri, Dou El Kefel Benkabou, Seif-Eddine Benabdeslem, Khalid Machine Learning Artificial Intelligence Fréchet regression extends linear regression to model complex responses in metric spaces, making it particularly relevant for multi-label regression, where eachinstance can have multiple associated labels. However, addressing noise and dependencies among predictors within this framework remains un derexplored. In this paper, we present an extension of the Global Fréchet re gression model that enables explicit modeling of relationships between input variables and multiple responses. To address challenges arising from noise and multicollinearity, we propose a novel framework based on implicit regu larization, which preserves the intrinsic structure of the data while effectively capturing complex dependencies. Our approach ensures accurate and efficient modeling without the biases introduced by traditional explicit regularization methods. Theoretical guarantees are provided, and the performance of the proposed method is demonstrated through numerical experiments. |
| title | Fréchet regression with implicit denoising and multicollinearity reduction |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2412.18247 |