Penalized orthogonal-components regression for large p small n data
Copyright policy )Penalized orthogonal-components regression for large p small n data
We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data.
12 pages
- Purdue University System United States
- TRUSTEES OF PURDUE UNIVERSITY United States
- Purdue University West Lafayette United States
- Purdue University Northwest United States
FOS: Computer and information sciences, latent-variable model, Ridge regression; shrinkage estimators (Lasso), Latent-variable model, Measures of association (correlation, canonical correlation, etc.), Empirical Bayes thresholding, empirical Bayes thresholding, Machine Learning (stat.ML), supervised dimension reduction, \(p\gg n\) data, Methodology (stat.ME), 62J07, Sparse predictors, 62J05, POCRE, Statistics - Machine Learning, p≫n data, General nonlinear regression, sparse predictors, Supervised dimension reduction, Statistics - Methodology, 62H20
FOS: Computer and information sciences, latent-variable model, Ridge regression; shrinkage estimators (Lasso), Latent-variable model, Measures of association (correlation, canonical correlation, etc.), Empirical Bayes thresholding, empirical Bayes thresholding, Machine Learning (stat.ML), supervised dimension reduction, \(p\gg n\) data, Methodology (stat.ME), 62J07, Sparse predictors, 62J05, POCRE, Statistics - Machine Learning, p≫n data, General nonlinear regression, sparse predictors, Supervised dimension reduction, Statistics - Methodology, 62H20
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