Prediction and Inference

Sparse Group Linear Models

After model fitting, you can perform prediction using fitted GVSSB model and new data, simply by calling the predict.GVSSB function:

n_test <- 50
X_test <- mvtnorm::rmvnorm(n_test, sigma=diag(p))
gvssb.predicted <- predict.GVSSB(gvssb.Laplace, X_test)

You may also get the volume of coverage region using the coverage function by specifying the fitted model, confidence level and inference type (group or marginal). If a coefficient vector is provided, it will also provide a vector of logical values indicating whether each coefficient (group) is selected as nonzero.

gvssb.coverage.group <- coverage(gvssb.Laplace, alpha = 0.95, beta = beta, type = "group")
gvssb.coverage.marginal <- coverage(gvssb.Laplace, alpha = 0.95, beta = beta, type = "marginal")

The returned value is a list:

• regionvol: A vector of region volumes with length $p$ (for group level) or $G$ (for marginal level)
• coverindex: A vector of logical values indicating whether each coefficient or group is selected. Has the same length as regionvol.

Sparse Additive Models

Similarly, the fitted AMSSB model can also be used to predict new data with predict.AMSSB:

n_test <- 50
X_test <- mvtnorm::rmvnorm(n_test, sigma = diag(G))
amssb.predicted <- predict.AMSSB(amssb.Laplace, X_test)

For a convenience visualization of the fitted AMSSB model, you can resort to plot.AMSSB given the coefficient index of interest:

plot.AMSSB(model.Laplace, index = 1)