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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1903.00037 |
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| _version_ | 1866914979143221248 |
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| author | Ni, Yijin Yu, Chuanping Ko, Andy Huo, Xiaoming |
| author_facet | Ni, Yijin Yu, Chuanping Ko, Andy Huo, Xiaoming |
| contents | This paper introduces a method called Sequential and Simultaneous Distance-based Dimension Reduction ($S^2D^2R$) that performs simultaneous dimension reduction for a pair of random vectors based on Distance Covariance (dCov). Compared with Sufficient Dimension Reduction (SDR) and Canonical Correlation Analysis (CCA)-based approaches, $S^2D^2R$ is a model-free approach that does not impose dimensional or distributional restrictions on variables and is more sensitive to nonlinear relationships. Theoretically, we establish a non-asymptotic error bound to guarantee the performance of $S^2D^2R$. Numerically, $S^2D^2R$ performs comparable to or better than other state-of-the-art algorithms and is computationally faster. All codes of our $S^2D^2R$ method can be found on Github, including an R package named S2D2R. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_00037 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Sequential and Simultaneous Distance-based Dimension Reduction Ni, Yijin Yu, Chuanping Ko, Andy Huo, Xiaoming Methodology This paper introduces a method called Sequential and Simultaneous Distance-based Dimension Reduction ($S^2D^2R$) that performs simultaneous dimension reduction for a pair of random vectors based on Distance Covariance (dCov). Compared with Sufficient Dimension Reduction (SDR) and Canonical Correlation Analysis (CCA)-based approaches, $S^2D^2R$ is a model-free approach that does not impose dimensional or distributional restrictions on variables and is more sensitive to nonlinear relationships. Theoretically, we establish a non-asymptotic error bound to guarantee the performance of $S^2D^2R$. Numerically, $S^2D^2R$ performs comparable to or better than other state-of-the-art algorithms and is computationally faster. All codes of our $S^2D^2R$ method can be found on Github, including an R package named S2D2R. |
| title | Sequential and Simultaneous Distance-based Dimension Reduction |
| topic | Methodology |
| url | https://arxiv.org/abs/1903.00037 |