Continuous Generalized Gradient Descent
CGGD is a method for calculating trajectories in high-dimensional
parameter spaces for variable selection and prediction in regression
models. Examples include proportional gradient shrinkage as an
extension of LASSO and LARS, threshold gradient descent with
right-continuous variable selectors, threshold ridge regression, and
many more with proper combinations of variable selectors and functional
forms of a kernel. In all these problems, general gradient descent
trajectories are continuous piecewise analytic vector-valued curves as
solutions to matrix differential equations. The algorithm is monotone
and converges in the loss or negative likelihood functions.
The paper: Continuous Generalized
Gradient Descent, Cun-Hui Zhang, Journal of Computational and Graphical
An R package that implements CGGD, written by Ofer Melnik and Cun-Hui
Zhang is available from CRAN.
The authors take no responsibility stated or implied for the contents,
use, applicability, or results of the CGGD software package.