# Robust Boosting for regression This function implements the RRBoost robust boosting algorithm for regression, as well as other robust and non-robust boosting algorithms for regression. ```r Boost( x_train, y_train, x_val, y_val, x_test, y_test, type = "RRBoost", error = c("rmse", "aad"), niter = 200, y_init = "LADTree", max_depth = 1, tree_init_provided = NULL, control = Boost.control() ) ``` ## Arguments - `x_train`: predictor matrix for training data (matrix/dataframe) - `y_train`: response vector for training data (vector/dataframe) - `x_val`: predictor matrix for validation data (matrix/dataframe) - `y_val`: response vector for validation data (vector/dataframe) - `x_test`: predictor matrix for test data (matrix/dataframe, optional, required when `make_prediction` in control is `TRUE`) - `y_test`: response vector for test data (vector/dataframe, optional, required when `make_prediction` in control is `TRUE`) - `type`: type of the boosting method: "L2Boost", "LADBoost", "MBoost", "Robloss", "SBoost", "RRBoost" (character string) - `error`: a character string (or vector of character strings) indicating the type of error metrics to be evaluated on the test set. Valid options are: "rmse" (root mean squared error), "aad" (average absolute deviation), and "trmse" (trimmed root mean squared error) - `niter`: number of boosting iterations (for RRBoost: T_1,max + T_2,max) (numeric) - `y_init`: a string indicating the initial estimator to be used. Valid options are: "median" or "LADTree" (character string) - `max_depth`: the maximum depth of the tree learners (numeric) - `tree_init_provided`: an optional pre-fitted initial tree (an `rpart` object) - `control`: a named list of control parameters, as returned by `Boost.control` ## Returns A list with the following components: - **type**: which boosting algorithm was run. One of: "L2Boost", "LADBoost", "MBoost", "Robloss", "SBoost", "RRBoost" (character string) - **control**: the list of control parameters used - **niter**: number of iterations for the boosting algorithm (for RRBoost T_1,max + T_2,max) (numeric) - **error**: if `make_prediction = TRUE` in argument `control`, a vector of prediction errors evaluated on the test set at early stopping time. The length of the vector matches that of the `error` argument in the input. - **tree_init**: if `y_init = "LADTree"`, the initial tree (an object of class `rpart`) - **tree_list**: if `save_tree = TRUE` in `control`, a list of trees fitted at each boosting iteration - **f_train_init**: a vector of the initialized estimator of the training data - **alpha**: a vector of base learners' coefficients - **early_stop_idx**: early stopping iteration - **when_init**: if `type = "RRBoost"`, the early stopping time of the first stage of RRBoost - **loss_train**: a vector of training loss values (one per iteration) - **loss_val**: a vector of validation loss values (one per iteration) - **err_val**: a vector of validation aad errors (one per iteration) - **err_train**: a vector of training aad errors (one per iteration) - **err_test**: a matrix of test errors before and at the early stopping iteration (returned if make_prediction = TRUE in control); the matrix dimension is the early stopping iteration by the number of error types (matches the `error` argument in the input); each row corresponds to the test errors at each iteration - **f_train**: a matrix of training function estimates at all iterations (returned if save_f = TRUE in control); each column corresponds to the fitted values of the predictor at each iteration - **f_val**: a matrix of validation function estimates at all iterations (returned if save_f = TRUE in control); each column corresponds to the fitted values of the predictor at each iteration - **f_test**: a matrix of test function estimatesbefore and at the early stopping iteration (returned if save_f = TRUE and make_prediction = TRUE in control); each column corresponds to the fitted values of the predictor at each iteration - **var_select**: a vector of variable selection indicators (one per explanatory variable; 1 if the variable was selected by at least one of the base learners, and 0 otherwise) - **var_importance**: a vector of permutation variable importance scores (one per explanatory variable, and returned if cal_imp = TRUE in control) ## Details This function implements a robust boosting algorithm for regression (RRBoost). It also includes the following robust and non-robust boosting algorithms for regression: L2Boost, LADBoost, MBoost, Robloss, and SBoost. This function uses the functions available in the `rpart` package to construct binary regression trees. ## Examples ```r data(airfoil) n <- nrow(airfoil) n0 <- floor( 0.2 * n ) set.seed(123) idx_test <- sample(n, n0) idx_train <- sample((1:n)[-idx_test], floor( 0.6 * n ) ) idx_val <- (1:n)[ -c(idx_test, idx_train) ] xx <- airfoil[, -6] yy <- airfoil$y xtrain <- xx[ idx_train, ] ytrain <- yy[ idx_train ] xval <- xx[ idx_val, ] yval <- yy[ idx_val ] xtest <- xx[ idx_test, ] ytest <- yy[ idx_test ] model_RRBoost_LADTree = Boost(x_train = xtrain, y_train = ytrain, x_val = xval, y_val = yval, x_test = xtest, y_test = ytest, type = "RRBoost", error = "rmse", y_init = "LADTree", max_depth = 1, niter = 10, ## to keep the running time low control = Boost.control(max_depth_init = 2, min_leaf_size_init = 20, make_prediction = TRUE, cal_imp = FALSE)) ``` ## See Also `Boost.validation`, `Boost.control`. ## Author(s) Xiaomeng Ju, xmengju@stat.ubc.ca

Boost function