# cv.SBGAM: Cross-Validation for Sparse Bayesian Generalized Additive... In sparseGAM: Sparse Generalized Additive Models

## Description

This function implements K-fold cross-validation for sparse Bayesian generalized additive models (GAMs) with the spike-and-slab group lasso (SSGL) penalty. The identity link function is used for Gaussian GAMs, the logit link is used for binomial GAMs, and the log link is used for Poisson, negative binomial, and gamma GAMs.

## Usage

 1 2 3 4 cv.SBGAM(y, X, df=6, family=c("gaussian","binomial","poisson","negativebinomial","gamma"), nb.size=1, gamma.shape=1, nfolds=5, nlambda0=20, lambda0, lambda1, a, b, max.iter=100, tol = 1e-6, print.fold=TRUE) 

## Arguments

 y n \times 1 vector of responses. X n \times p design matrix, where the jth column of X corresponds to the jth overall covariate. df number of B-spline basis functions to use in each basis expansion. Default is df=6, but the user may specify degrees of freedom as any integer greater than or equal to 3. family exponential dispersion family. Allows for "gaussian", "binomial", "poisson", "negativebinomial", and "gamma". Note that for "negativebinomial", the size parameter must be specified, while for "gamma", the shape parameter must be specified. nb.size known size parameter α in NB(α,μ_i) distribution for negative binomial responses. Default is nb.size=1. Ignored if family is not "negativebinomial". gamma.shape known shape parameter ν in Gamma(μ_i,ν) distribution for gamma responses. Default is gamma.shape=1. Ignored if family is not "gamma". nfolds number of folds K to use in K-fold cross-validation. Default is nfolds=5. nlambda0 number of spike hyperparameter L. Default is nlambda0=20. lambda0 grid of L spike hyperparameters λ_0. The user may specify either a scalar or a vector. If the user does not provide this, the program chooses the grid automatically. lambda1 slab hyperparameter λ_1 in the SSGL prior. Default is lambda1=1. a shape hyperparameter for the Beta(a,b) prior on the mixing proportion in the SSGL prior. Default is a=1. b shape hyperparameter for the Beta(a,b) prior on the mixing proportion in the SSGL prior. Default is b=dim(X)[2]. max.iter maximum number of iterations in the algorithm. Default is max.iter=100. tol convergence threshold for algorithm. Default is tol=1e-6. print.fold Boolean variable for whether or not to print the current fold in the algorithm. Default is print.fold=TRUE.

## Value

The function returns a list containing the following components:

 lambda0 L \times 1 vector of spike hyperparameters lambda0 used to fit the model. lambda0 is displayed in descending order. cve L \times 1 vector of mean cross-validation error across all K folds. The kth entry in cve corresponds to the kth regularization parameter in lambda0. cvse L \times 1 vector of standard errors for cross-validation error across all K folds. The kth entry in cvse corresponds to the kth regularization parameter in lambda0. lambda0.min value of lambda0 that minimizes mean cross-validation error cve.

## References

Bai R. (2021). "Spike-and-slab group lasso for consistent Bayesian estimation and variable selection in non-Gaussian generalized additive models." arXiv pre-print arXiv:2007.07021.

Bai, R., Moran, G. E., Antonelli, J. L., Chen, Y., and Boland, M.R. (2021). "Spike-and-slab group lassos for grouped regression and sparse generalized additive models." Journal of the American Statistical Association, in press.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ## Generate data set.seed(12345) X = matrix(runif(30*3), nrow=30) n = dim(X)[1] y = 2.5*sin(pi*X[,1]) + rnorm(n) ## K-fold cross-validation for 4 degrees of freedom and 4 values of lambda0 ## Note that if user does not specify lambda0, cv.SBGAM chooses a grid automatically. cv.mod = cv.SBGAM(y, X, df=4, family="gaussian", lambda0=seq(from=25,to=5,by=-10)) ## Plot CVE curve plot(cv.mod$lambda0, cv.mod$cve, type="l", xlab="lambda0", ylab="CVE") ## lambda which minimizes cross-validation error cv.mod\$lambda0.min 

sparseGAM documentation built on May 31, 2021, 5:09 p.m.