Package 'TSLA' reference manual

Title:	Tree-Guided Rare Feature Selection and Logic Aggregation
Description:	Implementation of the tree-guided feature selection and logic aggregation approach introduced in Chen et al. (2024) <doi:10.1080/01621459.2024.2326621>. The method enables the selection and aggregation of large-scale rare binary features with a known hierarchical structure using a convex, linearly-constrained regularized regression framework. The package facilitates the application of this method to both linear regression and binary classification problems by solving the optimization problem via the smoothing proximal gradient descent algorithm (Chen et al. (2012) <doi:10.1214/11-AOAS514>).
Authors:	Jianmin Chen [aut, cre], Kun Chen [aut]
Maintainer:	Jianmin Chen <jianminc000@gmail.com>
License:	GPL-3
Version:	0.1.2
Built:	2025-03-17 22:20:13 UTC
Source:	CRAN

Tree-Guided Rare Feature Selection and Logic Aggregation

Description

This package provides functions and visualization tools for fitting the Tree-Guided Rare Feature Selection and Logic Aggregation model.

Author(s)

Jianmin Chen jianminc000@gmail.com, Kun Chen

Calculate group norms

Description

Function to output group norms on the gamma coefficients based on g_idx and C2 matrix.

Usage

cal2norm(u, g_idx, type)
cal2norm(u, g_idx, type)

Arguments

`u`	`C2*gamma.coef`, `gamma.coef` is the estimated node coefficient vector, `C2` matrix is the output from function `get_tree_object()`, which gives the weights of the groups.
`g_idx`	Group structure matrix defined by the `C2` matrix. See details in `get_tree_object()`.
`type`	If `type == 1`, return sum of group norms; else return individual norm for each group.

Value

Sum of group norms or individual group norms.

Synthesic for the classification example

Description

Synthetic data used to illustrate how to use TSLA with classification.

Usage

data(ClassificationExample)
data(ClassificationExample)

Format

List containing the following elements:

tree.org: Original tree structure with 42 leaf nodes and 5 different levels.
x.org: Original design matrix with 42 binary features and 400 observations.
x1: Unpenalized covariate.
y: Continuous response of length 400.

Get coefficients from a fitted TSLA model

Description

Get coefficients from a TSLA.fit object.

Usage

coef_TSLA(object, ...)
coef_TSLA(object, ...)

Arguments

`object`	A fit output from `TSLA.fit()`.
`...`	Other parameters.

Value

A list of coefficients for each combination of $\lambda$ and $\alpha$ . The first dimension is indexed by the coefficient, the second dimension is indexed by $\lambda$ , and the third dimension is indexed by $\alpha$ .

`Intercept`	Intercept.
`cov.coef`	Coefficients for unpenalized features.
`gamma.coef`	Node coefficients. Also see details in `getetmat()`.
`beta.coef`	Regression coefficients. Each coefficient is multiplied by $(-1)^{r-1}$ , where r is the order of the corresponding interaction term. Also see details in `getetmat()`.
`beta.coef.adj`	Regression coefficients $\beta$ . This is the common regression coefficient vector. It corresponds to `x.expand.adj` and `A.adj`.

Cross validation for TSLA

Description

Conduct cross validation to select the optimal tuning parameters in TSLA.

Usage

cv.TSLA(
  y,
  X_1 = NULL,
  X_2,
  treemat,
  family = c("ls", "logit"),
  penalty = c("CL2", "RFS-Sum"),
  pred.loss = c("MSE", "AUC", "deviance"),
  gamma.init = NULL,
  weight = NULL,
  nfolds = 5,
  group.weight = NULL,
  feature.weight = NULL,
  control = list(),
  modstr = list()
)
cv.TSLA(
  y,
  X_1 = NULL,
  X_2,
  treemat,
  family = c("ls", "logit"),
  penalty = c("CL2", "RFS-Sum"),
  pred.loss = c("MSE", "AUC", "deviance"),
  gamma.init = NULL,
  weight = NULL,
  nfolds = 5,
  group.weight = NULL,
  feature.weight = NULL,
  control = list(),
  modstr = list()
)

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".
`pred.loss`	Model performance metrics. If `family="ls"`, default is "MSE" (mean squared error). If `family="logit"`, default is "AUC". For logistic model, another option is "deviance".
`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.
`nfolds`	Number of cross validation folds. Default is 5.
`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.

Value

A list of cross validation results.

`lambda.min`	$\lambda$ value with best prediction performance.
`alpha.min`	$\alpha$ value with best prediction performance.
`cvm`	A (number-of-lambda * number-of-alpha) matrix saving the means of cross validation loss across folds.
`cvsd`	A (number-of-lambda * number-of-alpha) matrix saving standard deviations of cross validation loss across folds.
`TSLA.fit`	Outputs from `TSLA.fit()`.
`Intercept.min`	Intercept corresponding to `(lambda.min,alpha.min)`.
`cov.min`	Coefficients of unpenalized features corresponding to `(lambda.min,alpha.min)`.
`beta.min`	Coefficients of binary features corresponding to `(lambda.min,alpha.min)`.
`gamma.min`	Node coefficients corresponding to `(lambda.min,alpha.min)`.
`groupnorm.min`	Group norms of node coefficients corresponding to `(lambda.min,alpha.min)`.
`lambda.min.index`	Index of the best $\lambda$ in the sequence.
`alpha.min.index`	Index of the best $\alpha$ in the sequence.

Examples

# Load the synthetic data
data(ClassificationExample)

tree.org <- ClassificationExample$tree.org   # original tree structure
x2.org <- ClassificationExample$x.org      # original design matrix
x1 <- ClassificationExample$x1
y <- ClassificationExample$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

# Do train-test split
idtrain <- 1:200
x1.train <- as.matrix(x1[idtrain, ])
x2.train <- x2[idtrain, ]
y.train <- y[idtrain, ]
x1.test <- as.matrix(x1[-idtrain, ])
x2.test <- x2[-idtrain, ]
y.test <- y[-idtrain, ]

# specify some model parameters
set.seed(100)
control <- list(maxit = 100, mu = 1e-3, tol = 1e-5, verbose = FALSE)
modstr <- list(nlambda = 5,  alpha = seq(0, 1, length.out = 5))
simu.cv <- cv.TSLA(y = y.train, as.matrix(x1[idtrain, ]),
                   X_2 = x2.train,
                   treemat = tree.expand, family = 'logit',
                   penalty = 'CL2', pred.loss = 'AUC',
                   gamma.init = NULL, weight = c(1, 1), nfolds = 5,
                   group.weight = NULL, feature.weight = NULL,
                   control = control, modstr =  modstr)
# Do prediction with the selected tuning parameters on the test set. Report AUC on the test set.
rmid <- simu.cv$TSLA.fit$rmid  # remove all zero columns
if(length(rmid) > 0){
  x2.test <- x2.test[, -rmid]}
  y.new <- predict_cvTSLA(simu.cv, as.matrix(x1[-idtrain, ]), x2.test)
  library(pROC)
  auc(as.vector(y.test), as.vector(y.new))


# Load the synthetic data
data(ClassificationExample)

tree.org <- ClassificationExample$tree.org   # original tree structure
x2.org <- ClassificationExample$x.org      # original design matrix
x1 <- ClassificationExample$x1
y <- ClassificationExample$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

# Do train-test split
idtrain <- 1:200
x1.train <- as.matrix(x1[idtrain, ])
x2.train <- x2[idtrain, ]
y.train <- y[idtrain, ]
x1.test <- as.matrix(x1[-idtrain, ])
x2.test <- x2[-idtrain, ]
y.test <- y[-idtrain, ]

# specify some model parameters
set.seed(100)
control <- list(maxit = 100, mu = 1e-3, tol = 1e-5, verbose = FALSE)
modstr <- list(nlambda = 5,  alpha = seq(0, 1, length.out = 5))
simu.cv <- cv.TSLA(y = y.train, as.matrix(x1[idtrain, ]),
                   X_2 = x2.train,
                   treemat = tree.expand, family = 'logit',
                   penalty = 'CL2', pred.loss = 'AUC',
                   gamma.init = NULL, weight = c(1, 1), nfolds = 5,
                   group.weight = NULL, feature.weight = NULL,
                   control = control, modstr =  modstr)
# Do prediction with the selected tuning parameters on the test set. Report AUC on the test set.
rmid <- simu.cv$TSLA.fit$rmid  # remove all zero columns
if(length(rmid) > 0){
  x2.test <- x2.test[, -rmid]}
  y.new <- predict_cvTSLA(simu.cv, as.matrix(x1[-idtrain, ]), x2.test)
  library(pROC)
  auc(as.vector(y.test), as.vector(y.new))

Tree-guided reparameterization

Description

This function generates all the intermediate quantities based on the tree-guided reparameterization.

Usage

get_tree_object(
  X_2,
  treemat,
  penalty = c("CL2", "DL2", "RFS-Sum"),
  group.weight = NULL,
  feature.weight = NULL
)
get_tree_object(
  X_2,
  treemat,
  penalty = c("CL2", "DL2", "RFS-Sum"),
  group.weight = NULL,
  feature.weight = NULL
)

Arguments

`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 for `penalty = "CL2"`; Original structure for `penalty = "RFS-Sum"`. Need to be in the matrix form.
`penalty`	Two options for group penalty on $\gamma$ , "CL2" or "RFS-Sum".
`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.

Value

A list consists of quantities needed for SPG optimization.

`C_1`	C_1 matrix for generalized lasso penalty.
`CNorm_1`	Nuclear norm of matrix `C_1`.
`C_2`	C_2 matrix for group lasso penalty.
`CNorm_2`	Nuclear norm of matrix `C_2`.
`A`	A (number-of-leaf * number-of-node) binary matrix containing linear constraints. Recall that $\beta=A\gamma$ . It is used with `beta.coef` and `x.expand`.
`g_idx`	A (number-of-group * 3) matrix. Each column stands for starting row in `C_2` of a group, end row in `C_2` of a group, and the group size.
`M2`	A (number-of-leaf * number-of-level) node index matrix, with index going from 1 to the number of nodes. Root node has index equal to the number of nodes. Each row corresponds to a variable at the finest level, each column corresponds to an ordered classification level; the entry values in each column are the unique indices of the variables at that level. As we move to the right, the number of unique values becomes fewer.
`Tree`	A (number-of-group * number-of-node) group index matrix. Each row is a group and the column order is the same as the order of node index in M2. If the jth node belongs to the ith group, then the (i, j) element of the matrix is 1; otherwise the element is 0.
`A.adj`	A (number-of-leaf * number-of-node) binary matrix containing linear constraints. It is used with `beta.coef.adj` and `x.expand.adj`.

Generate aggregated features

Description

Function that generates aggregated features based on the TSLA output.

Usage

getaggr(TSLA.object, X_2, X_2.org, lambda.index, alpha.index)
getaggr(TSLA.object, X_2, X_2.org, lambda.index, alpha.index)

Arguments

`TSLA.object`	A fit output from `TSLA.fit()`, or the `TSLA.fit` object in `cv.TSLA()`.
`X_2`	Expanded design matrix in matrix form.
`X_2.org`	Original design matrix in matrix form.
`lambda.index`	Index of the $\lambda$ value selected.
`alpha.index`	Index of the $\alpha$ value selected. The $\alpha$ is the tuning parameter for generalized lasso penalty.

Value

A data.frame of the aggregated feature.

dataset

aggregated features.

Tree-guided expansion

Description

Give the expanded design matrix and the expanded tree structure by adding interactions in conformity to the structure.

Usage

getetmat(tmatrix, dmatrix)
getetmat(tmatrix, dmatrix)

Arguments

`tmatrix`	Tree structure of the original features in matrix form.
`dmatrix`	Original design matrix in matrix form.

Details

This function is used by the TSLA method only when the penalty is selected as "CL2". The all zero columns produced by the interactions are excluded in the output.

For the TSLA method, the signs of the coefficients in the linear constraints depend on the order of the term. To better extend the method in implementation, we apply the signs on the feature vectors instead of the regression coefficients. For example, we use feature vector - $x_{12}$ instead of $x_{12}$ . The expanded design matrix x.expand from this function is adjusted by the signs. The A matrix and all the coefficients estimated from the package can be explained correspondingly. We also provide x.expand.adj, A.adj, and beta.coef.adj as the quantities with the effects of the signs removed.

The input tree structure of the original features needs to be constructed as the following: each row corresponds to a variable at the finest level; each column corresponds to an ordered classification level with the leaf level at the left-most and the root level at the right-most; the entry values in each column are the index of the ancestor node of the variable at that level. As we move from left to right, the number of unique values in the column becomes fewer.

Value

A list.

`x.expand`	The design matrix after expansion. Each column is multiplied by $(-1)^{r-1}$ , where r is the order of the corresponding interaction term.
`tree.expand`	The tree structure after expansion.
`x.expand.adj`	The design matrix after expansion with the effects of signs removed.

Get performance metrics for classification

Description

Evaluate the prediction performance under the classification settings.

Usage

getperform(
  ytest,
  ypretest,
  family,
  threshold.method = c("youden", "specificity.control", "quantile"),
  specificity = NULL
)
getperform(
  ytest,
  ypretest,
  family,
  threshold.method = c("youden", "specificity.control", "quantile"),
  specificity = NULL
)

Arguments

`ytest`	Response vector for test data.
`ypretest`	Predicted probability for test data.
`family`	"ls" or "logic". Return MSE when "ls" is used.
`threshold.method`	Method to get the threshold.
`specificity`	User-defined specificity or quantile.

Details

The function supports three methods to select the threshold of the predicted probability.

threshold.method = "youden": The optimal threshold corresponds to the point that maximizes the distance to the identity (diagonal) line on the ROC curve.

threshold.method = "specificity.control": The optimal threshold corresponds to the smallest value that ensures the required specificity value.

threshold.method = "quantile": The optimal threshold corresponds to the required quantile of the predicted probability.

Value

List of measures.

`AUC`	Area under the ROC curve.
`AUPRC`	Area under the precision-recall curve.
`threshold`	Selected threshold of the probability.
`sensitivity`	Sensitivity with the selected threshold.
`ppv`	Positive predictive value with the selected threshold.
`specificity`	Specificity with the selected threshold.
`true.positive`	Number of true positive with the selected threshold.
`false.positive`	Number of false positive with the selected threshold.

Plot aggregated structure

Description

Return a tree plot.

Usage

plot_TSLA(TSLA.object, X_2, X_2.org, lambda.index, alpha.index)
plot_TSLA(TSLA.object, X_2, X_2.org, lambda.index, alpha.index)

Arguments

`TSLA.object`	A fit output from `TSLA.fit()`, or the `TSLA.fit` object in `cv.TSLA()`.
`X_2`	Expanded design matrix in matrix form.
`X_2.org`	Original design matrix in matrix form.
`lambda.index`	Index of the $\lambda$ value selected.
`alpha.index`	Index of the $\alpha$ value selected. The $\alpha$ is the tuning parameter for generalized lasso penalty.

Value

A plot

Examples

# Load the synthetic data
data(ClassificationExample)

tree.org <- ClassificationExample$tree.org   # original tree structure
x2.org <- ClassificationExample$x.org      # original design matrix
x1 <- ClassificationExample$x1
y <- ClassificationExample$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

# Do train-test split
idtrain <- 1:200
x1.train <- as.matrix(x1[idtrain, ])
x2.train <- x2[idtrain, ]
y.train <- y[idtrain, ]
x1.test <- as.matrix(x1[-idtrain, ])
x2.test <- x2[-idtrain, ]
y.test <- y[-idtrain, ]

# specify some model parameters
set.seed(100)
control <- list(maxit = 100, mu = 1e-3, tol = 1e-5, verbose = FALSE)
modstr <- list(nlambda = 5,  alpha = seq(0, 1, length.out = 5))
simu.cv <- cv.TSLA(y = y.train, as.matrix(x1[idtrain, ]),
                   X_2 = x2.train,
                   treemat = tree.expand, family = 'logit',
                   penalty = 'CL2', pred.loss = 'AUC',
                   gamma.init = NULL, weight = c(1, 1), nfolds = 5,
                   group.weight = NULL, feature.weight = NULL,
                   control = control, modstr =  modstr)
plot_TSLA(simu.cv$TSLA.fit, x2, x2.org, simu.cv$lambda.min.index, simu.cv$alpha.min.index)



# Load the synthetic data
data(ClassificationExample)

tree.org <- ClassificationExample$tree.org   # original tree structure
x2.org <- ClassificationExample$x.org      # original design matrix
x1 <- ClassificationExample$x1
y <- ClassificationExample$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

# Do train-test split
idtrain <- 1:200
x1.train <- as.matrix(x1[idtrain, ])
x2.train <- x2[idtrain, ]
y.train <- y[idtrain, ]
x1.test <- as.matrix(x1[-idtrain, ])
x2.test <- x2[-idtrain, ]
y.test <- y[-idtrain, ]

# specify some model parameters
set.seed(100)
control <- list(maxit = 100, mu = 1e-3, tol = 1e-5, verbose = FALSE)
modstr <- list(nlambda = 5,  alpha = seq(0, 1, length.out = 5))
simu.cv <- cv.TSLA(y = y.train, as.matrix(x1[idtrain, ]),
                   X_2 = x2.train,
                   treemat = tree.expand, family = 'logit',
                   penalty = 'CL2', pred.loss = 'AUC',
                   gamma.init = NULL, weight = c(1, 1), nfolds = 5,
                   group.weight = NULL, feature.weight = NULL,
                   control = control, modstr =  modstr)
plot_TSLA(simu.cv$TSLA.fit, x2, x2.org, simu.cv$lambda.min.index, simu.cv$alpha.min.index)

Prediction from cross validation

Description

A convenient function to get prediction from the selected tuning parameters by cross validation.

Usage

predict_cvTSLA(
  object,
  X_1_new = NULL,
  X_2_new,
  type = c("response", "link"),
  ...
)
predict_cvTSLA(
  object,
  X_1_new = NULL,
  X_2_new,
  type = c("response", "link"),
  ...
)

Arguments

`object`	A fit output from `cv.TSLA().`
`X_1_new`	New unpenalized features in matrix form.
`X_2_new`	New binary features in matrix form.
`type`	Two options: "response" or "link". The two options only differ for `family="logit"`.
`...`	Other parameters.

Value

Predictions.

Prediction from TSLA with new data

Description

Generate prediction for the response.

Usage

predict_TSLA(
  object,
  X_1_new = NULL,
  X_2_new,
  type = c("response", "link"),
  ...
)
predict_TSLA(
  object,
  X_1_new = NULL,
  X_2_new,
  type = c("response", "link"),
  ...
)

Arguments

`object`	A fit output from `TSLA.fit()`.
`X_1_new`	New unpenalized features in matrix form.
`X_2_new`	New binary features in matrix form.
`type`	Two options: "response" or "link". The two options only differ for `family="logit"`.
`...`	Other parameters.

Value

Predictions. The first dimension is indexed by the observation, the second dimension is indexed by $\lambda$ , and the third dimension is indexed by $\alpha$ .

Synthesic for the regression example

Description

Synthetic data used to illustrate how to use TSLA with regression.

Usage

data(RegressionExample)
data(RegressionExample)

Format

List containing the following elements:

tree.org: Original tree structure with 42 leaf nodes and 5 different levels.
x.org: Original design matrix with 42 binary features and 400 observations.
y: Continuous response of length 400.

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()
)
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()
)

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".

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()`.

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, 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, 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, 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
# 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

Package 'TSLA'

Help Index

Tree-Guided Rare Feature Selection and Logic Aggregation

Description

Author(s)

Calculate group norms

Description

Usage

Arguments

Value

Synthesic for the classification example

Description

Usage

Format

Get coefficients from a fitted TSLA model

Description

Usage

Arguments

Value

Cross validation for TSLA

Description

Usage

Arguments

Value

Examples

Tree-guided reparameterization

Description

Usage

Arguments

Value

Generate aggregated features

Description

Usage

Arguments

Value

Tree-guided expansion

Description

Usage

Arguments

Details

Value

Get performance metrics for classification

Description

Usage

Arguments

Details

Value

Plot aggregated structure

Description

Usage

Arguments

Value

Examples

Prediction from cross validation

Description

Usage

Arguments

Value

Prediction from TSLA with new data

Description

Usage

Arguments

Value

Synthesic for the regression example

Description

Usage

Format

Solve the TSLA optimization problem

Description

Usage

Arguments

Details

Value

References

Examples