sparselink (version 1.0.0)

construct_penfacs: Construct penalty factors

Description

Uses internal and external weights as well as internal and external exponents or factors for these weights to construct penalty factors.

Usage

construct_penfacs(w_int, w_ext, v_int, v_ext, type)

Value

Returns a vector of length \(q\) (non-negative entries).

Arguments

w_int

internal weights: numeric vector of length \(p\) with non-negative entries

w_ext

external weights: numeric vector of length \(p\) with non-negative entries

v_int

exponent or factor for internal weights: non-negative scalar

v_ext

exponent or factor for external weights: non-negative scalar

type

scaling of weights: character "exp", "ari", "geo", or "rem" (with or without addition of ".con"), default: "exp"

Details

While internal weights are from the problem of interest ("supported" problem), external weights are from the other problems ("supporting" problems).

Multiple options exist for scaling prior weights:

• "exp": \(w_{int}^{v_{int}}+w_{ext}^{v_{ext}}\)

• "ari": \(v_{int} w_{int} + v_{ext} w_{ext}\)

• "geo": \(w_{int}^{v_{int}} w_{ext}^{v_{ext}}\)

• "rem": \(w_{int}^{v_{int}}+w_{ext}^{v_{ext}}-\mathbb{I}(v_{int}=0)-\mathbb{I}(v_{ext}=0))\)

The constrained versions "exp.con", "ari.con", "geo.con", and "rem.con" impose \(v_{int}+v_{ext}=1\). The penalty factors are the inverse weights. Suggested choices are "exp" for predictivity and "ari.con" for interpretability.

See Also

Use construct_weights to obtain w_int and w_ext.

Examples

n <- 10
w_int <- stats::runif(n)
w_ext <- stats::runif(n)
construct_penfacs(w_int,w_ext,v_int=0.5,v_ext=0.5,type="exp")