# Cross validation for TSLA Conduct cross validation to select the optimal tuning parameters in TSLA. ```r 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. ## Returns 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 ```r # 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)) ```

cv.TSLA function