Volume 21, Issue 4 (12-2024)                   jor 2024, 21(4): 1-14 | Back to browse issues page

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Kazemi M. Group Descent Algorithm in Penalized Nonparametric Additive Model. jor 2024; 21 (4) :1-14
URL: http://jamlu.liau.ac.ir/article-1-2163-en.html
Group Descent Algorithm in Penalized Nonparametric Additive Model
M. Kazemi *
Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran , m.kazemi@guilan.ac.ir
Abstract:   (491 Views)
Nonparametric additive model is one of the common models for modeling the relationship between variables. In this paper, we consider the high-dimensional nonparametric additive model in which the number of explanatory variables can exceed the number of observations, but the number of important explanatory variables relative to the number of observations is small. When the number of explanatory variables in the model is large, model interpretation becomes more difficult and computational costs increase. Therefore, identifying the explanatory variables that have a significant impact on the response or non-zero additive components in this model is crucial. To this end, we first approximate the additive components using B-spline bases. By employing this approximation, the problem of variable selection is transformed into selecting groups of non-zero coefficients. Then, we use grouped penalty functions for selecting non-zero coefficients. This is usually done by minimizing the sum of squared errors subject to a constraint. Minimizing this target function requires the use of optimization methods. In this paper, we utilize a group descent algorithm to solve the aforementioned minimization problem. Finally, the performance of this algorithm is examined under three different penalty functions through simulation studies and analysis of a real dataset.
 
Keywords: Group Variable Selection, High-dimensional Data, Nonparametric Additive Model, Optimization.
Full-Text [PDF 1115 kb]   (127 Downloads)    
Type of Study: Research | Subject: Special
Received: 2024/06/22 | Accepted: 2024/11/14 | Published: 2024/12/21
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