prox: Composite proximal operator based on L2, L2-Square, and L1 penalties
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. \(\lambda_1\) and
\(\lambda_2\) are L2 and L2-Square (ridge) penalties for \(x\) in
a group level, and \(\lambda_3\) 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,
\(\lambda_2\) and \(\lambda_3\) are forced to be zeroes; when
hierarchy=1, \(\lambda_2\) is forced to be zero; when
hierarchy=2, there is no constraint on \(\lambda\)'s.
See smog.
d
indices for overlapped variables in x.
Value
A two-dimensional numerical vector, soft-thresholded based on a composition of
\(\lambda_1\), \(\lambda_2\), and \(\lambda_3\).