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Principal component‐guided sparse regression
Author(s) -
Tay Jingyi K.,
Friedman Jerome,
Tibshirani Robert
Publication year - 2021
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11617
Subject(s) - principal component analysis , lasso (programming language) , sparse pca , feature (linguistics) , feature selection , artificial intelligence , pattern recognition (psychology) , principal component regression , coefficient matrix , component (thermodynamics) , computer science , quadratic equation , matrix (chemical analysis) , group (periodic table) , mathematics , eigenvalues and eigenvectors , world wide web , linguistics , philosophy , physics , geometry , materials science , organic chemistry , chemistry , quantum mechanics , composite material , thermodynamics
We propose a new method for supervised learning, the “ principal components lasso ” (“pcLasso”). It combines the lasso ( ℓ 1 ) penalty with a quadratic penalty that shrinks the coefficient vector toward the feature matrix's leading principal components (PCs). pcLasso can be especially powerful if the features are preassigned to groups. In that case, pcLasso shrinks each group‐wise component of the solution toward the leading PCs of that group. The pcLasso method also carries out selection of feature groups. We provide some theory and illustrate the method on some simulated and real data examples.