Enhancing Sufficient Dimension Reduction via Hellinger Correlation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913370167312384 |
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| author | Hong, Seungbeom Kim, Ilmun Song, Jun |
| author_facet | Hong, Seungbeom Kim, Ilmun Song, Jun |
| contents | In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated by the recent introduction of the Hellinger correlation as a dependency measure. Utilizing this measure, we develop a method capable of effectively detecting the dimension reduction subspace, complete with theoretical justification. Through extensive numerical experiments, we demonstrate that our proposed method significantly enhances and outperforms existing SDR methods. This improvement is largely attributed to our proposed method's deeper understanding of data dependencies and the refinement of existing SDR techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enhancing Sufficient Dimension Reduction via Hellinger Correlation Hong, Seungbeom Kim, Ilmun Song, Jun Machine Learning Methodology In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated by the recent introduction of the Hellinger correlation as a dependency measure. Utilizing this measure, we develop a method capable of effectively detecting the dimension reduction subspace, complete with theoretical justification. Through extensive numerical experiments, we demonstrate that our proposed method significantly enhances and outperforms existing SDR methods. This improvement is largely attributed to our proposed method's deeper understanding of data dependencies and the refinement of existing SDR techniques. |
| title | Enhancing Sufficient Dimension Reduction via Hellinger Correlation |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2405.19704 |