A Tree-Based Multiscale Regression Method
A tree-based method for regression is proposed. In a high dimensional feature space, the method has the ability to adapt to the lower intrinsic dimension of data if the data possess such a property so that reliable statistical estimates can be performed without being hindered by the “curse of dimens...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2018-12-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/article/10.3389/fams.2018.00063/full |
| _version_ | 1819047929678135296 |
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| author | Haiyan Cai Qingtang Jiang |
| author_facet | Haiyan Cai Qingtang Jiang |
| author_sort | Haiyan Cai |
| collection | DOAJ |
| description | A tree-based method for regression is proposed. In a high dimensional feature space, the method has the ability to adapt to the lower intrinsic dimension of data if the data possess such a property so that reliable statistical estimates can be performed without being hindered by the “curse of dimensionality.” The method is also capable of producing a smoother estimate for a regression function than those from standard tree methods in the region where the function is smooth and also being more sensitive to discontinuities of the function than smoothing splines or other kernel methods. The estimation process in this method consists of three components: a random projection procedure that generates partitions of the feature space, a wavelet-like orthogonal system defined on a tree that allows for a thresholding estimation of the regression function based on that tree and, finally, an averaging process that averages a number of estimates from independently generated random projection trees. |
| first_indexed | 2024-12-21T11:08:10Z |
| format | Article |
| id | doaj.art-70700da6779f4b468ae6c6d5687e379c |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-21T11:08:10Z |
| publishDate | 2018-12-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-70700da6779f4b468ae6c6d5687e379c2022-12-21T19:06:10ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872018-12-01410.3389/fams.2018.00063429494A Tree-Based Multiscale Regression MethodHaiyan CaiQingtang JiangA tree-based method for regression is proposed. In a high dimensional feature space, the method has the ability to adapt to the lower intrinsic dimension of data if the data possess such a property so that reliable statistical estimates can be performed without being hindered by the “curse of dimensionality.” The method is also capable of producing a smoother estimate for a regression function than those from standard tree methods in the region where the function is smooth and also being more sensitive to discontinuities of the function than smoothing splines or other kernel methods. The estimation process in this method consists of three components: a random projection procedure that generates partitions of the feature space, a wavelet-like orthogonal system defined on a tree that allows for a thresholding estimation of the regression function based on that tree and, finally, an averaging process that averages a number of estimates from independently generated random projection trees.https://www.frontiersin.org/article/10.3389/fams.2018.00063/fullregressionnon-linearhigh dimension datatree methodsmultiscale (MS) modelingmanifold learning |
| spellingShingle | Haiyan Cai Qingtang Jiang A Tree-Based Multiscale Regression Method Frontiers in Applied Mathematics and Statistics regression non-linear high dimension data tree methods multiscale (MS) modeling manifold learning |
| title | A Tree-Based Multiscale Regression Method |
| title_full | A Tree-Based Multiscale Regression Method |
| title_fullStr | A Tree-Based Multiscale Regression Method |
| title_full_unstemmed | A Tree-Based Multiscale Regression Method |
| title_short | A Tree-Based Multiscale Regression Method |
| title_sort | tree based multiscale regression method |
| topic | regression non-linear high dimension data tree methods multiscale (MS) modeling manifold learning |
| url | https://www.frontiersin.org/article/10.3389/fams.2018.00063/full |
| work_keys_str_mv | AT haiyancai atreebasedmultiscaleregressionmethod AT qingtangjiang atreebasedmultiscaleregressionmethod AT haiyancai treebasedmultiscaleregressionmethod AT qingtangjiang treebasedmultiscaleregressionmethod |