visualize.shrink: Plots grpnet Shrinkage Operator or its Estimator

In grpnet: Group Elastic Net Regularized GLMs and GAMs

Plots grpnet Shrinkage Operator or its Estimator

Description

Makes a plot or returns a data frame containing the group elastic net shrinkage operator (or its estimator) evaluated at a sequence of input values.

Usage

visualize.shrink(x = seq(-5, 5, length.out = 1001), 
                penalty = c("LASSO", "MCP", "SCAD"), 
                alpha = 1, 
                lambda = 1, 
                gamma = 4, 
                fitted = FALSE,
                plot = TRUE,
                subtitle = TRUE,
                legend = TRUE,
                location = "top",
                ...)

Arguments

x	sequence of values at which to evaluate the penalty.
penalty	which penalty or penalties should be plotted?
alpha	elastic net tuning parameter (between 0 and 1).
lambda	overall tuning parameter (non-negative).
gamma	additional hyperparameter for MCP (>1) or SCAD (>2).
fitted	if FALSE (default), then the shrinkage operator is plotted; otherwise the shrunken estimator is plotted.
plot	if TRUE (default), then the result is plotted; otherwise the result is returned as a data frame.
subtitle	if TRUE (default), then the hyperparameter values are displayed in the subtitle.
legend	if TRUE (default), then a legend is included to distinguish the different penalty types.
location	the legend's location; ignored if legend = FALSE.
...	addition arguments passed to plot function, e.g., xlim, ylim, etc.

Details

The updates for the group elastic net estimator have the form

\boldsymbol\beta_{\alpha, \lambda}^{(t+1)} = S_{\lambda_1, \lambda_2}(\|\mathbf{b}_{\alpha, \lambda}^{(t+1)}\|) \mathbf{b}_{\alpha, \lambda}^{(t+1)}

where S_{\lambda_1, \lambda_2}(\cdot) is a shrinkage and selection operator, and

\mathbf{b}_{\alpha, \lambda}^{(t+1)} = \boldsymbol\beta_{\alpha, \lambda}^{(t)} + (\delta_{(t)} \epsilon)^{-1} \mathbf{g}^{(t)}

is the unpenalized update with \mathbf{g}^{(t)} denoting the current gradient.

Note that \lambda_1 = \lambda \alpha is the L1 tuning parameter, \lambda_2 = \lambda (1-\alpha) is the L2 tuning parameter, \delta_{(t)} is an upper-bound on the weights appearing in the Fisher information matrix, and \epsilon is the largest eigenvalue of the Gramm matrix n^{-1} \mathbf{X}^\top \mathbf{X}.

Value

If plot = TRUE, then produces a plot.

If plot = FALSE, then returns a data frame.

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

Fan J, & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456), 1348-1360. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/016214501753382273")}

Helwig, N. E. (2024). Versatile descent algorithms for group regularization and variable selection in generalized linear models. Journal of Computational and Graphical Statistics. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2024.2362232")}

Tibshirani, R. (1996). Regression and shrinkage via the Lasso. Journal of the Royal Statistical Society, Series B, 58, 267-288. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.2517-6161.1996.tb02080.x")}

Zhang CH (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38(2), 894-942. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/09-AOS729")}

See Also

visualize.penalty for plotting penalty function

Examples

# plot shrinkage operator
visualize.shrink()

# plot shrunken estimator
visualize.shrink(fitted = TRUE)

grpnet documentation built on Oct. 12, 2024, 1:07 a.m.