ppmSDR: Penalized Principal Machine for Sufficient Dimension Reduction

A unified, computation-friendly framework for penalized principal machines (P2M), a class of sparse sufficient dimension reduction (SDR) estimators for regression and binary classification. Principal machines (PM) estimate the central subspace by solving a family of convex-loss problems over several cutoffs; their penalized counterparts (P2M) add a row-group sparsity penalty so that dimension reduction and variable selection are performed simultaneously. All estimators are fitted by a single group coordinate descent (GCD) algorithm that accommodates least squares, logistic, asymmetric least squares, L2-hinge, hinge (support vector machine, SVM) and quantile losses, together with the least absolute shrinkage and selection operator (LASSO), the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP). Methods are described in Li, Artemiou and Li (2011) <doi:10.1214/11-AOS932>, Shin and Artemiou (2017) <doi:10.1016/j.csda.2016.12.003>, Artemiou, Dong and Shin (2021) <doi:10.1016/j.patcog.2020.107768> and Breheny and Huang (2015) <doi:10.1007/s11222-013-9424-2>.

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