TSLA (version 0.1.2)

TSLA.fit: Solve the TSLA optimization problem

Description

Find the solutions with a Smoothing Proximal Gradient (SPG) algorithm for a sequence of \(\alpha\) and \(\lambda\) values.

Usage

TSLA.fit(
  y,
  X_1 = NULL,
  X_2,
  treemat,
  family = c("ls", "logit"),
  penalty = c("CL2", "RFS-Sum"),
  gamma.init = NULL,
  weight = NULL,
  group.weight = NULL,
  feature.weight = NULL,
  control = list(),
  modstr = list()
)

Value

A list of model fitting results.

gammacoef

Estimation for \(\gamma\).

groupnorm

Weighted norms for each group.

lambda.seq

Sequence of \(\lambda\) values.

alpha.seq

Tuning parameter sequence for the generalized lasso penalty.

rmid

Column index for all zero features.

family

Option of family.

cov.name

Names for unpenalized features.

bin.name

Names for binary feautres.

tree.object

Outputs from get_tree_obj().

Arguments

y

Response in matrix form, continuous for family = "ls" and binary (0/1) for family = "logit".

X_1

Design matrix for unpenalized features (excluding intercept). Need to be in the matrix form.

X_2

Expanded design matrix for penalty = "CL2"; Original design matrix for penalty = "RFS-Sum". Need to be in the matrix form.

treemat

Expanded tree structure in matrix form for penalty = "CL2"; Original structure for penalty = "RFS-Sum".

family

Two options. Use "ls" for least square problems and "logit" for logistic regression problems.

penalty

Two options for group penalty on \(\gamma\), "CL2" or "RFS-Sum".

gamma.init

Initial value for the optimization. Default is a zero vector. The length should equal to 1+ncol(X_1)+ncol(A). See details of A in get_tree_obj().

weight

A vector of length two and it is used for logistic regression only. The first element corresponds to weight of y=1 and the second element corresponds to weight of y=0.

group.weight

User-defined weights for group penalty. Need to be a vector and the length equals to the number of groups.

feature.weight

User-defined weights for each predictor after expansion.

control

A list of parameters controlling algorithm convergence. Default values: tol = 1e-5, convergence tolerance; maxit = 10000, maximum number of iterations; mu = 1e-3, smoothness parameter in SPG.

modstr

A list of parameters controlling tuning parameters. Default values: lambda = NULL. If lambda is not provided, the package will give a default lambda sequence; lambda.min.ratio = 1e-04, smallest value for lambda as a fraction of lambda.max (given by default when lambda is NULL); nlambda = 50, number of lambda values (equal spacing on log scale) used when lambda is NULL; alpha = seq(0, 1, length.out = 10), sequence of alpha. Here, alpha is tuning parameter for generalized lasso penalty and 1-alpha is the tuning parameter for group lasso penalty.

Details

We adopt the warm start technique to speed up the calculation. The warm start is applied with a fixed value of \(\alpha\) and a descending sequence of \(\lambda\).

The objective function for "ls" is $$1/2 RSS+\lambda(\alpha P(\beta)+(1-\alpha) P(\gamma)),$$ subject to \(\beta=A\gamma\). The objective function for "logit" is $$-loglik + \lambda(\alpha P(\beta)+(1-\alpha) P(\gamma)),$$ subject to \(\beta=A\gamma\). Note that, in this package, the input parameter "alpha" is the tuning parameter for the generalized lasso penalty.

Details for "penalty" option:

For penalty = "CL2", see details for the "Child-l2" penalty in the main paper.

For penalty = "RFS-Sum", the theoretical optimal weights are used. Please check the details in paper "Rare feature selection in high dimensions".

References

Chen, J., Aseltine, R. H., Wang, F., & Chen, K. (2024). Tree-Guided Rare Feature Selection and Logic Aggregation with Electronic Health Records Data. Journal of the American Statistical Association 119(547), 1765-1777, tools:::Rd_expr_doi("10.1080/01621459.2024.2326621").
Chen, X., Q. Lin, S. Kim, J. G. Carbonell, and E. P. Xing (2012). Smoothing proximal gradient method for general structured sparse regression. The Annals of Applied Statistics 6(2), 719–752, tools:::Rd_expr_doi("10.1214/11-AOAS514").
Yan, X. and J. Bien (2021). Rare feature selection in high dimensions. Journal of the American Statistical Association 116(534), 887–900, tools:::Rd_expr_doi("10.1080/01621459.2020.1796677").

Examples

# Load the synthetic data
data(RegressionExample)

tree.org <- RegressionExample$tree.org   # original tree structure
x2.org <- RegressionExample$x.org      # original design matrix
y <- RegressionExample$y            # response

# Do the tree-guided expansion
expand.data <- getetmat(tree.org, x2.org)
x2 <- expand.data$x.expand              # expanded design matrix
tree.expand <- expand.data$tree.expand  # expanded tree structure

# specify some model parameters
set.seed(100)
control <- list(maxit = 100, mu = 1e-3, tol = 1e-5, verbose = FALSE)
# fit model with a pair of lambda and alpha
modstr <- list(lambda = 1,  alpha = 0.1)
x1 <- NULL
fit1 <- TSLA.fit(y, x1, x2, tree.expand, family = 'ls',
                 penalty = 'CL2',
                 gamma.init = NULL, weight = NULL,
                 group.weight = NULL, feature.weight = NULL,
                 control, modstr)
# get group norms from fit1
fit1$groupnorm