LASSO ISOtone for High Dimensional Additive Isotonic Regression
Additive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are monotonically increasing. In this article, we present a new method...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1797079692897943552 |
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| author | Fang, Z Meinshausen, N |
| author_facet | Fang, Z Meinshausen, N |
| author_sort | Fang, Z |
| collection | OXFORD |
| description | Additive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are monotonically increasing. In this article, we present a new method for such regression called LASSO Isotone (LISO). LISO adapts ideas from sparse linear modelling to additive isotonic regression. Thus, it is viable in many situations with high dimensional predictor variables, where selection of significant versus insignificant variables are required. We suggest an algorithm involving a modification of the backfitting algorithm CPAV. We give a numerical convergence result, and finally examine some of its properties through simulations. We also suggest some possible extensions that improve performance, and allow calculation to be carried out when the direction of the monotonicity is unknown. |
| first_indexed | 2024-03-07T00:49:24Z |
| format | Journal article |
| id | oxford-uuid:85da0771-ea71-4734-bf71-5d16938633d6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:49:24Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:85da0771-ea71-4734-bf71-5d16938633d62022-03-26T22:00:09ZLASSO ISOtone for High Dimensional Additive Isotonic RegressionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:85da0771-ea71-4734-bf71-5d16938633d6EnglishSymplectic Elements at Oxford2010Fang, ZMeinshausen, NAdditive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are monotonically increasing. In this article, we present a new method for such regression called LASSO Isotone (LISO). LISO adapts ideas from sparse linear modelling to additive isotonic regression. Thus, it is viable in many situations with high dimensional predictor variables, where selection of significant versus insignificant variables are required. We suggest an algorithm involving a modification of the backfitting algorithm CPAV. We give a numerical convergence result, and finally examine some of its properties through simulations. We also suggest some possible extensions that improve performance, and allow calculation to be carried out when the direction of the monotonicity is unknown. |
| spellingShingle | Fang, Z Meinshausen, N LASSO ISOtone for High Dimensional Additive Isotonic Regression |
| title | LASSO ISOtone for High Dimensional Additive Isotonic Regression |
| title_full | LASSO ISOtone for High Dimensional Additive Isotonic Regression |
| title_fullStr | LASSO ISOtone for High Dimensional Additive Isotonic Regression |
| title_full_unstemmed | LASSO ISOtone for High Dimensional Additive Isotonic Regression |
| title_short | LASSO ISOtone for High Dimensional Additive Isotonic Regression |
| title_sort | lasso isotone for high dimensional additive isotonic regression |
| work_keys_str_mv | AT fangz lassoisotoneforhighdimensionaladditiveisotonicregression AT meinshausenn lassoisotoneforhighdimensionaladditiveisotonicregression |