RMSS {RMSS}

Robust Multi-Model Subset Selection

Description

RMSS performs robust multi-model subset selection.

Usage

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
)

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.

Value

An object of class RMSS

Author(s)

Anthony-Alexander Christidis, [e-mail]

See Also

coef.RMSS, predict.RMSS

Examples

# 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
}

# RMSS
rmss_fit <- 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)
rmss_coefs <- coef(rmss_fit, 
                   h_ind = 1, t_ind = 2, u_ind = 1,
                   group_index = 1:rmss_fit$n_models)
sens_rmss <- sum(which((rmss_coefs[-1]!=0)) <= p.active)/p.active
spec_rmss <- sum(which((rmss_coefs[-1]!=0)) <= p.active)/sum(rmss_coefs[-1]!=0)
rmss_preds <- predict(rmss_fit, newx = x_test,
                      h_ind = 1, t_ind = 2, u_ind = 1,
                      group_index = 1:rmss_fit$n_models,
                      dynamic = FALSE)
rmss_mspe <- mean((y_test - rmss_preds)^2)/sigma^2