prox: Composite proximal operator based on L2, L2-Square, and L1...

In smog: Structural Modeling by using Overlapped Group Penalty

Description

Composite proximal operator based on L2, L2-Square, and L1 penalties

Usage

prox(x, lambda, hierarchy, d)

Arguments

x	A numeric vector of two.
lambda	a vector of three penalty parameters. λ_1 and λ_2 are L2 and L2-Square (ridge) penalties for x in a group level, and λ_3 is the L1 penalty for x_2, respectively.
hierarchy	a factor value in levels 0, 1, 2, which represent different hierarchical structure in x, respectively. When hierarchy=0, λ_2 and λ_3 are forced to be zeroes; when hierarchy=1, λ_2 is forced to be zero; when hierarchy=2, there is no constraint on λ's. See smog.
d	indices for overlapped variables in x.

Value

A two-dimensional numerical vector, soft-thresholded based on a composition of λ_1, λ_2, and λ_3.

Author(s)

Chong Ma, [e-mail].

References

\insertRef

ma2019structuralsmog

See Also

cv.smog, smog.default, smog.formula, predict.smog, plot.smog.

Examples

prox(x = rnorm(6,2,1), lambda = c(0.5,0.3,0.1), hierarchy = 0, d = c(1,1,2,2,3,3))

smog documentation built on Aug. 10, 2020, 5:07 p.m.