prox: Proximal operator for nuclear norm

In npmr: Nuclear Penalized Multinomial Regression

Proximal operator for nuclear norm

Description

Return the value of the proximal operator of the nuclear norm (scaled by threshold) applied to a matrix

Usage

prox(B, threshold, group)

Arguments

B	matrix
threshold	scaling factor applied to the nuclear norm. In proximal gradient descent for NPMR, this is the product of the stepsize and the regularization parameter lambda
group	Vector of length equal to number of variables, i.e. 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.

Value

the value of the proximal operator of the nuclear norm (scaled by threshold) applied to B

Author(s)

Scott Powers, Trevor Hastie, Rob Tibshirani

References

Neal Parikh and Stephen Boyd (2013) “Proximal algorithms.” Foundations and Trends in Optimization 1, 3:123-231.

See Also

nuclear, PGDnpmr

npmr documentation built on Nov. 12, 2023, 1:08 a.m.