# Cross-Validatoin for Robust Multi-Model Subset Selection `cv.RMSS` performs the cross-validation procedure for robust multi-model subset selection. ```r cv.RMSS( x, y, n_models, h_grid, t_grid, u_grid, initial_estimator = c("robStepSplitReg", "srlars")[1], tolerance = 0.1, max_iter = 1000, neighborhood_search = FALSE, neighborhood_search_tolerance = 0.1, cv_criterion = c("tau", "trimmed")[1], n_folds = 5, alpha = 1/4, gamma = 1, n_threads = 1 ) ``` ## Arguments - `x`: Design matrix. - `y`: Response vector. - `n_models`: Number of models into which the variables are split. - `h_grid`: Grid for robustness parameter. - `t_grid`: Grid for sparsity parameter. - `u_grid`: Grid for diversity parameter. - `initial_estimator`: Method used for initial estimator. Must be one of "robStepSplitReg" (default) or "srlars". - `tolerance`: Tolerance level for convergence of PSBGD algorithm. - `max_iter`: Maximum number of iterations in PSBGD algorithm. - `neighborhood_search`: Neighborhood search to improve solution. Default is FALSE. - `neighborhood_search_tolerance`: Tolerance parameter for neighborhood search. Default is 1e-1. - `cv_criterion`: Criterion to use for cross-validation procedure. Must be one of "tau" (default) or "trimmed". - `n_folds`: Number of folds for cross-validation procedure. Default is 5. - `alpha`: Proportion of trimmed samples for cross-validation procedure. Default is 1/4. - `gamma`: Weight parameter for ensemble MSPE (gamma) and average MSPE of individual models (1 - gamma). Only used if "cv_criterion" is set to "trimmed". Default is 1. - `n_threads`: Number of threads used by OpenMP for multithreading over the folds. Default is 1. ## Returns An object of class cv.RMSS ## Examples ```r # Simulation parameters n <- 50 p <- 100 rho <- 0.8 rho.inactive <- 0.2 group.size <- 5 p.active <- 15 snr <- 2 contamination.prop <- 0.3 # Setting the seed set.seed(0) # Block Correlation sigma.mat <- matrix(0, p, p) sigma.mat[1:p.active, 1:p.active] <- rho.inactive for(group in 0:(p.active/group.size - 1)) sigma.mat[(group*group.size+1):(group*group.size+group.size), (group*group.size+1):(group*group.size+group.size)] <- rho diag(sigma.mat) <- 1 # Simulation of beta vector true.beta <- c(runif(p.active, 0, 5)*(-1)^rbinom(p.active, 1, 0.7), rep(0, p - p.active)) # Setting the SD of the variance sigma <- as.numeric(sqrt(t(true.beta) %*% sigma.mat %*% true.beta)/sqrt(snr)) # Simulation of test data m <- 2e3 x_test <- mvnfast::rmvn(m, mu = rep(0, p), sigma = sigma.mat) y_test <- x_test %*% true.beta + rnorm(m, 0, sigma) # Simulation of uncontaminated data x <- mvnfast::rmvn(n, mu = rep(0, p), sigma = sigma.mat) y <- x %*% true.beta + rnorm(n, 0, sigma) # Contamination of data contamination_indices <- 1:floor(n*contamination.prop) k_lev <- 2 k_slo <- 100 x_train <- x y_train <- y beta_cont <- true.beta beta_cont[true.beta!=0] <- beta_cont[true.beta!=0]*(1 + k_slo) beta_cont[true.beta==0] <- k_slo*max(abs(true.beta)) for(cont_id in contamination_indices){ a <- runif(p, min = -1, max = 1) a <- a - as.numeric((1/p)*t(a) %*% rep(1, p)) x_train[cont_id,] <- mvnfast::rmvn(1, rep(0, p), 0.1^2*diag(p)) + k_lev * a / as.numeric(sqrt(t(a) %*% solve(sigma.mat) %*% a)) y_train[cont_id] <- t(x_train[cont_id,]) %*% beta_cont } # CV RMSS rmss_fit <- cv.RMSS(x = x_train, y = y_train, n_models = 3, h_grid = c(35), t_grid = c(6, 8, 10), u_grid = c(1:3), initial_estimator = "robStepSplitReg", tolerance = 1e-1, max_iter = 1e3, neighborhood_search = FALSE, neighborhood_search_tolerance = 1e-1, n_folds = 5, alpha = 1/4, gamma = 1, n_threads = 1) rmss_coefs <- coef(rmss_fit, h_ind = rmss_fit$h_opt, t_ind = rmss_fit$t_opt, u_ind = rmss_fit$u_opt, group_index = 1:rmss_fit$n_models) sens_rmss <- sum(which((rmss_coefs[-1]!=0)) <= p.active)/p.active spec_rmss <- sum(which((rmss_coefs[-1]!=0)) <= p.active)/sum(rmss_coefs[-1]!=0) rmss_preds <- predict(rmss_fit, newx = x_test, h_ind = rmss_fit$h_opt, t_ind = rmss_fit$t_opt, u_ind = rmss_fit$u_opt, group_index = 1:rmss_fit$n_models, dynamic = FALSE) rmss_mspe <- mean((y_test - rmss_preds)^2)/sigma^2 ``` ## See Also `coef.cv.RMSS`, `predict.cv.RMSS` ## Author(s) Anthony-Alexander Christidis, anthony.christidis@stat.ubc.ca

cv.RMSS function