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>.
