grpnet (version 0.5)

visualize.penalty: Plots grpnet Penalty Function or its Derivative

Description

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

Usage

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

Value

If plot = TRUE, then produces a plot.

If plot = FALSE, then returns a data frame.

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).

derivative

if FALSE (default), then the penalty is plotted; otherwise the derivative of the penalty 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.

Author

Nathaniel E. Helwig <[e-mail]>

Details

The group elastic net penalty is defined as $$P_{\alpha, \lambda}(\boldsymbol\beta) = Q_{\lambda_1}(\|\boldsymbol\beta\|) + \frac{\lambda_2}{2} \|\boldsymbol\beta\|^2$$ where \(Q_\lambda()\) denotes the L1 penalty (LASSO, MCP, or SCAD), \(\| \boldsymbol\beta \| = (\boldsymbol\beta^\top \boldsymbol\beta)^{1/2}\) denotes the Euclidean norm, \(\lambda_1 = \lambda \alpha\) is the L1 tuning parameter, and \(\lambda_2 = \lambda (1-\alpha)\) is the L2 tuning parameter. Note that \(\lambda\) and \(\alpha\) denote the lambda and alpha arguments.

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. 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. 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. 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. tools:::Rd_expr_doi("10.1214/09-AOS729")

See Also

visualize.shrink for plotting shrinkage operator

Examples

# plot penalty functions
visualize.penalty()

# plot penalty derivatives
visualize.penalty(derivative = TRUE)