LASSO Isotone for High-Dimensional Additive Isotonic Regression
By Zhou Fang, Nicolai Meinshausen. 2010
23 citations recorded by the source corpus.
Additive isotonic regression attempts to determine the relationship between a multidimensional 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 modeling to additive isotonic regression. Thus, it is viable in many situations with high-dimensional predictor variables, where selection of significant versus insignificant variables is 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. Supplemental materials are available online for this article.
Subfields: Analytical Chemistry, Statistics and Probability
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In Analytical Chemistry
In Statistics and Probability
- Yining Chen
- Richard J. Samworth
- Arlene K. H. Kim
- Bodhisattva Sen
- John D. Lafferty
- Minhua Chen
- Min Xu
- David B. Dunson
Citations in the corpus
- Generalized additive and index models with shape constraints (2014, background): “…papers studying additive isotonic regression, including Bacchetti (1989), Morton-Jones et al. (2000), Tutz and Leitenstorfer (2007), Cai and Dunson (2007), Mammen and Yu (2007), Brezger and Steiner (2008), Cheng (2009), Cheng et al. (2012), Fang and Meinshausen (2012), Rueda (2013) and Yu (2014).”