PGDnpmr: Proximal gradient descent for nuclear penalized multinomial regression

Description

Iterates steps of proximal gradient descent until convergence, by repeatedly taking steps in the direction of the negative of the gradient and soft-thresholding the singular values of the result. Intended for internal use only.

Usage

PGDnpmr(B, b, X, Y, lambda, s, group = NULL, accelerated = TRUE, eps = 1e-07,
    maxit = 1e+05, quiet = TRUE)

Value

B: Optimal value of the regression coeffient matrix at convergence
b: Optimal value of the regression intercept vector at convergence
objectivePath: Vector showing the value of the objective function at each step in proximal gradient descent
time: Time taken until convergence

Arguments

B: Initial regression coefficient matrix
b: Initial intercept vector
X: Covariate matrix. May be in sparse form from Matrix package
Y: Response matrix. Each row has exactly one 1 indicating response category for that observation. All other entries are zero.
lambda: Vector of regularization parameter values for penalizing nuclear norm
s: Step size for proximal gradient descent
group: Vector of length equal to number of variables (ncol(X) and nrow(B)). Variables in the same group indexed by a POSITIVE integer will be penalized together (the nuclear norm of the sub-matrix of the regression coefficients will be penalized). Variables without positive integers will NOT be penalized. Default is NULL, which means there are no sub-groups; nuclear norm of entire coefficient matrix is penalized.
accelerated: Logical. Should accelerated proximal gradient descent be used? Default is TRUE.
eps: Convergence threshold. When relative change in the objective function after an interation drops below this threshold, algorithm halts.
maxit: Maximum number of iterations for proximal gradient descent.
quiet: Logical. Should output be silenced? If not, print the value of the objective function after each step of proximal gradient descent. Perhaps useful for debugging. Default is TRUE.

Author

Scott Powers, Trevor Hastie, Rob Tibshirani

References